An, Jing; Henderson, Christopher; Ryzhik, Lenya Voting models and semilinear parabolic equations. (English) Zbl 07778902 Nonlinearity 36, No. 11, 6104-6123 (2023). MSC: 35K57 35K58 60J80 PDFBibTeX XMLCite \textit{J. An} et al., Nonlinearity 36, No. 11, 6104--6123 (2023; Zbl 07778902) Full Text: DOI arXiv OA License
An, Jing; Henderson, Christopher; Ryzhik, Lenya Quantitative steepness, semi-FKPP reactions, and pushmi-pullyu fronts. (English) Zbl 07754928 Arch. Ration. Mech. Anal. 247, No. 5, Paper No. 88, 84 p. (2023). MSC: 35K57 35B40 35C07 35K15 PDFBibTeX XMLCite \textit{J. An} et al., Arch. Ration. Mech. Anal. 247, No. 5, Paper No. 88, 84 p. (2023; Zbl 07754928) Full Text: DOI arXiv
Drivas, Theodore D.; Dunlap, Alexander; Graham, Cole; La, Joonhyun; Ryzhik, Lenya Invariant measures for stochastic conservation laws on the line. (English) Zbl 07726739 Nonlinearity 36, No. 9, 4553-4584 (2023). Reviewer: Fanfei Meng (Beijing) MSC: 37L40 37L55 35R60 60H15 PDFBibTeX XMLCite \textit{T. D. Drivas} et al., Nonlinearity 36, No. 9, 4553--4584 (2023; Zbl 07726739) Full Text: DOI arXiv
Kiselev, Alexander; Nazarov, Fedor; Ryzhik, Lenya; Yao, Yao Chemotaxis and reactions in biology. (English) Zbl 1519.92032 J. Eur. Math. Soc. (JEMS) 25, No. 7, 2641-2696 (2023). MSC: 92C17 35K57 35K40 35K55 PDFBibTeX XMLCite \textit{A. Kiselev} et al., J. Eur. Math. Soc. (JEMS) 25, No. 7, 2641--2696 (2023; Zbl 1519.92032) Full Text: DOI arXiv
Dunlap, Alexander; Ryzhik, Lenya Branching Brownian motion with generation-dependent diffusivity and nonlocal partial differential equations. arXiv:2312.17139 Preprint, arXiv:2312.17139 [math.AP] (2023). MSC: 35K57 60J85 60J70 BibTeX Cite \textit{A. Dunlap} and \textit{L. Ryzhik}, ``Branching Brownian motion with generation-dependent diffusivity and nonlocal partial differential equations'', Preprint, arXiv:2312.17139 [math.AP] (2023) Full Text: arXiv OA License
Berestycki, Julien; Brunet, Éric; Graham, Cole; Mytnik, Leonid; Roquejoffre, Jean-Michel; Ryzhik, Lenya The distance between the two BBM leaders. (English) Zbl 1484.35262 Nonlinearity 35, No. 4, 1558-1609 (2022). MSC: 35K57 60J80 PDFBibTeX XMLCite \textit{J. Berestycki} et al., Nonlinearity 35, No. 4, 1558--1609 (2022; Zbl 1484.35262) Full Text: DOI arXiv
Mytnik, Leonid; Roquejoffre, Jean-Michel; Ryzhik, Lenya Fisher-KPP equation with small data and the extremal process of branching Brownian motion. (English) Zbl 1481.60182 Adv. Math. 396, Article ID 108106, 58 p. (2022). MSC: 60J80 60J65 35R60 60G50 PDFBibTeX XMLCite \textit{L. Mytnik} et al., Adv. Math. 396, Article ID 108106, 58 p. (2022; Zbl 1481.60182) Full Text: DOI arXiv
Dunlap, Alexander; Ryzhik, Lenya Viscous shock solutions to the stochastic Burgers equation. (English) Zbl 1481.35275 Arch. Ration. Mech. Anal. 242, No. 2, 937-971 (2021). Reviewer: Feng-Yu Wang (Swansea) MSC: 35L67 35K65 35R60 PDFBibTeX XMLCite \textit{A. Dunlap} and \textit{L. Ryzhik}, Arch. Ration. Mech. Anal. 242, No. 2, 937--971 (2021; Zbl 1481.35275) Full Text: DOI arXiv
Dunlap, Alexander; Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer The random heat equation in dimensions three and higher: the homogenization viewpoint. (English) Zbl 1481.35031 Arch. Ration. Mech. Anal. 242, No. 2, 827-873 (2021). MSC: 35B27 35K05 35K15 35R60 PDFBibTeX XMLCite \textit{A. Dunlap} et al., Arch. Ration. Mech. Anal. 242, No. 2, 827--873 (2021; Zbl 1481.35031) Full Text: DOI arXiv
Papanicolaou, George; Ryzhik, Lenya; Velcheva, Katerina Traveling waves in a mean field learning model. (English) Zbl 1469.91033 Nonlinearity 34, No. 10, 6799-6842 (2021). MSC: 91B62 91A16 35C07 35Q91 PDFBibTeX XMLCite \textit{G. Papanicolaou} et al., Nonlinearity 34, No. 10, 6799--6842 (2021; Zbl 1469.91033) Full Text: DOI arXiv
Mueller, Carl; Mytnik, Leonid; Ryzhik, Lenya The speed of a random front for stochastic reaction-diffusion equations with strong noise. (English) Zbl 1466.35005 Commun. Math. Phys. 384, No. 2, 699-732 (2021). MSC: 35A18 35K57 35K15 35R60 PDFBibTeX XMLCite \textit{C. Mueller} et al., Commun. Math. Phys. 384, No. 2, 699--732 (2021; Zbl 1466.35005) Full Text: DOI arXiv
Dunlap, Alexander; Graham, Cole; Ryzhik, Lenya Stationary solutions to the stochastic Burgers equation on the line. (English) Zbl 1470.60180 Commun. Math. Phys. 382, No. 2, 875-949 (2021). MSC: 60H15 35R60 35Q35 35Q53 82D60 PDFBibTeX XMLCite \textit{A. Dunlap} et al., Commun. Math. Phys. 382, No. 2, 875--949 (2021; Zbl 1470.60180) Full Text: DOI arXiv
Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya Fractional diffusion limit for a kinetic equation with an interface. (English) Zbl 1452.35212 Ann. Probab. 48, No. 5, 2290-2322 (2020). MSC: 35Q79 60J76 45A05 35R11 26A33 PDFBibTeX XMLCite \textit{T. Komorowski} et al., Ann. Probab. 48, No. 5, 2290--2322 (2020; Zbl 1452.35212) Full Text: DOI arXiv Euclid
An, Jing; Ryzhik, Lenya Global well-posedness for the Euler alignment system with mildly singular interactions. (English) Zbl 1445.35239 Nonlinearity 33, No. 9, 4670-4698 (2020). MSC: 35L45 35L60 35R09 35R11 35Q31 PDFBibTeX XMLCite \textit{J. An} and \textit{L. Ryzhik}, Nonlinearity 33, No. 9, 4670--4698 (2020; Zbl 1445.35239) Full Text: DOI arXiv
Dunlap, Alexander; Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer Fluctuations of the solutions to the KPZ equation in dimensions three and higher. (English) Zbl 1445.35345 Probab. Theory Relat. Fields 176, No. 3-4, 1217-1258 (2020). MSC: 35R60 60H07 60H15 PDFBibTeX XMLCite \textit{A. Dunlap} et al., Probab. Theory Relat. Fields 176, No. 3--4, 1217--1258 (2020; Zbl 1445.35345) Full Text: DOI arXiv
Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya The Bramson delay in the non-local Fisher-KPP equation. (English. French summary) Zbl 1436.35239 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 37, No. 1, 51-77 (2020). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35K57 45K05 35Q92 35C07 PDFBibTeX XMLCite \textit{E. Bouin} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 37, No. 1, 51--77 (2020; Zbl 1436.35239) Full Text: DOI arXiv
Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya Refined long-time asymptotics for Fisher-KPP fronts. (English) Zbl 1423.35208 Commun. Contemp. Math. 21, No. 7, Article ID 1850072, 25 p. (2019). MSC: 35K57 35B40 35C07 35K91 PDFBibTeX XMLCite \textit{J. Nolen} et al., Commun. Contemp. Math. 21, No. 7, Article ID 1850072, 25 p. (2019; Zbl 1423.35208) Full Text: DOI arXiv
Gu, Yu; Ryzhik, Lenya; Zeitouni, Ofer The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher. (English) Zbl 1400.82131 Commun. Math. Phys. 363, No. 2, 351-388 (2018). MSC: 82C05 35R60 82B44 60F17 60K37 60G15 35Q79 PDFBibTeX XMLCite \textit{Y. Gu} et al., Commun. Math. Phys. 363, No. 2, 351--388 (2018; Zbl 1400.82131) Full Text: DOI arXiv
Gu, Yu; Komorowski, Tomasz; Ryzhik, Lenya Fluctuations of random semilinear advection equations. (English) Zbl 1409.60149 SIAM J. Math. Anal. 50, No. 5, 5293-5336 (2018). MSC: 60K37 35R60 PDFBibTeX XMLCite \textit{Y. Gu} et al., SIAM J. Math. Anal. 50, No. 5, 5293--5336 (2018; Zbl 1409.60149) Full Text: DOI arXiv
Do, Tam; Kiselev, Alexander; Ryzhik, Lenya; Tan, Changhui Global regularity for the fractional Euler alignment system. (English) Zbl 1390.35370 Arch. Ration. Mech. Anal. 228, No. 1, 1-37 (2018). MSC: 35Q92 92C15 35Q31 35R11 35B36 35B65 PDFBibTeX XMLCite \textit{T. Do} et al., Arch. Ration. Mech. Anal. 228, No. 1, 1--37 (2018; Zbl 1390.35370) Full Text: DOI arXiv
Chen, Thomas; Komorowski, Tomasz; Ryzhik, Lenya The weak coupling limit for the random Schrödinger equation: the average wave function. (English) Zbl 1384.35117 Arch. Ration. Mech. Anal. 227, No. 1, 387-422 (2018). MSC: 35Q55 35R60 35R09 PDFBibTeX XMLCite \textit{T. Chen} et al., Arch. Ration. Mech. Anal. 227, No. 1, 387--422 (2018; Zbl 1384.35117) Full Text: DOI arXiv
Gu, Yu; Komorowski, Tomasz; Ryzhik, Lenya The Schrödinger equation with spatial white noise: the average wave function. (English) Zbl 1384.35105 J. Funct. Anal. 274, No. 7, 2113-2138 (2018). MSC: 35Q41 60J65 35R60 60H15 PDFBibTeX XMLCite \textit{Y. Gu} et al., J. Funct. Anal. 274, No. 7, 2113--2138 (2018; Zbl 1384.35105) Full Text: DOI arXiv
Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya Super-linear spreading in local and non-local cane toads equations. (English. French summary) Zbl 1375.35565 J. Math. Pures Appl. (9) 108, No. 5, 724-750 (2017). MSC: 35Q92 45K05 35B99 92D25 92D40 PDFBibTeX XMLCite \textit{E. Bouin} et al., J. Math. Pures Appl. (9) 108, No. 5, 724--750 (2017; Zbl 1375.35565) Full Text: DOI arXiv
Bouin, Emeric; Henderson, Christopher; Ryzhik, Lenya The bramson logarithmic delay in the cane toads equations. (English) Zbl 1370.35175 Q. Appl. Math. 75, No. 4, 599-634 (2017). MSC: 35K57 45K05 35C07 35Q92 PDFBibTeX XMLCite \textit{E. Bouin} et al., Q. Appl. Math. 75, No. 4, 599--634 (2017; Zbl 1370.35175) Full Text: DOI arXiv
Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya Convergence to a single wave in the Fisher-KPP equation. (English) Zbl 1365.35074 Chin. Ann. Math., Ser. B 38, No. 2, 629-646 (2017). MSC: 35K57 35C07 35B40 PDFBibTeX XMLCite \textit{J. Nolen} et al., Chin. Ann. Math., Ser. B 38, No. 2, 629--646 (2017; Zbl 1365.35074) Full Text: DOI arXiv
Gu, Yu; Ryzhik, Lenya The random Schrödinger equation: slowly decorrelating time-dependent potentials. (English) Zbl 1367.35139 Commun. Math. Sci. 15, No. 2, 359-378 (2017). MSC: 35Q41 35B27 35R60 60J65 35C20 PDFBibTeX XMLCite \textit{Y. Gu} and \textit{L. Ryzhik}, Commun. Math. Sci. 15, No. 2, 359--378 (2017; Zbl 1367.35139) Full Text: DOI arXiv
Kiselev, Alexander; Ryzhik, Lenya; Yao, Yao; Zlatoš, Andrej Finite time singularity for the modified SQG patch equation. (English) Zbl 1360.35159 Ann. Math. (2) 184, No. 3, 909-948 (2016). Reviewer: Alpár R. Mészáros (Los Angeles) MSC: 35Q31 35Q86 35B65 76B03 86A05 PDFBibTeX XMLCite \textit{A. Kiselev} et al., Ann. Math. (2) 184, No. 3, 909--948 (2016; Zbl 1360.35159) Full Text: DOI arXiv Link
Bal, Guillaume; Pinaud, Olivier; Ryzhik, Lenya On the stability of some imaging functionals. (English) Zbl 1348.35311 Inverse Probl. Imaging 10, No. 3, 585-616 (2016). MSC: 35R30 78A48 PDFBibTeX XMLCite \textit{G. Bal} et al., Inverse Probl. Imaging 10, No. 3, 585--616 (2016; Zbl 1348.35311) Full Text: DOI arXiv
Ignatova, Mihaela; Kukavica, Igor; Ryzhik, Lenya The Harnack inequality for second-order parabolic equations with divergence-free drifts of low regularity. (English) Zbl 1343.35047 Commun. Partial Differ. Equations 41, No. 2, 208-226 (2016). Reviewer: Vincenzo Vespri (Firenze) MSC: 35B45 35B35 35B65 35K10 35Q35 PDFBibTeX XMLCite \textit{M. Ignatova} et al., Commun. Partial Differ. Equations 41, No. 2, 208--226 (2016; Zbl 1343.35047) Full Text: DOI
Gomez, Christophe; Pinaud, Olivier; Ryzhik, Lenya Hypoelliptic estimates in radiative transfer. (English) Zbl 1342.35206 Commun. Partial Differ. Equations 41, No. 1, 150-184 (2016). MSC: 35Q20 35F10 35H10 35B65 35Q41 82C70 PDFBibTeX XMLCite \textit{C. Gomez} et al., Commun. Partial Differ. Equations 41, No. 1, 150--184 (2016; Zbl 1342.35206) Full Text: DOI
Gu, Yu; Ryzhik, Lenya The random Schrödinger equation: homogenization in time-dependent potentials. (English) Zbl 1339.60079 Multiscale Model. Simul. 14, No. 1, 323-363 (2016). MSC: 60H15 60F05 35R60 35J10 35B27 34E05 PDFBibTeX XMLCite \textit{Y. Gu} and \textit{L. Ryzhik}, Multiscale Model. Simul. 14, No. 1, 323--363 (2016; Zbl 1339.60079) Full Text: DOI arXiv
Hamel, François; Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya The logarithmic delay of KPP fronts in a periodic medium. (English) Zbl 1338.35243 J. Eur. Math. Soc. (JEMS) 18, No. 3, 465-505 (2016). Reviewer: Philippe Laurençot (Toulouse) MSC: 35K57 35B40 35C07 PDFBibTeX XMLCite \textit{F. Hamel} et al., J. Eur. Math. Soc. (JEMS) 18, No. 3, 465--505 (2016; Zbl 1338.35243) Full Text: DOI arXiv
Rodríguez, Nancy; Ryzhik, Lenya Exploring the effects of social preference, economic disparity, and heterogeneous environments on segregation. (English) Zbl 1336.35194 Commun. Math. Sci. 14, No. 2, 363-387 (2016). Reviewer: Rodica Luca (Iaşi) MSC: 35K55 35K57 35K65 35Q91 91C99 PDFBibTeX XMLCite \textit{N. Rodríguez} and \textit{L. Ryzhik}, Commun. Math. Sci. 14, No. 2, 363--387 (2016; Zbl 1336.35194) Full Text: DOI
Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya Power-like delay in time inhomogeneous Fisher-KPP equations. (English) Zbl 1327.35184 Commun. Partial Differ. Equations 40, No. 3, 475-505 (2015). Reviewer: Denise Huet (Nancy) MSC: 35K57 35B40 35C07 PDFBibTeX XMLCite \textit{J. Nolen} et al., Commun. Partial Differ. Equations 40, No. 3, 475--505 (2015; Zbl 1327.35184) Full Text: DOI
Bal, Guillaume; Pinaud, Olivier; Ryzhik, Lenya; Sølna, Knut Precursors for waves in random media. (English) Zbl 1456.74009 Wave Motion 51, No. 8, 1237-1253 (2014). MSC: 74A40 35Q41 35B25 35J05 35P25 PDFBibTeX XMLCite \textit{G. Bal} et al., Wave Motion 51, No. 8, 1237--1253 (2014; Zbl 1456.74009) Full Text: DOI
Komorowski, Tomasz; Novikov, Alexei; Ryzhik, Lenya Homogenization driven by a fractional Brownian motion: the shear layer case. (English) Zbl 1320.35046 Multiscale Model. Simul. 12, No. 2, 440-457 (2014). MSC: 35B27 76M50 60J65 PDFBibTeX XMLCite \textit{T. Komorowski} et al., Multiscale Model. Simul. 12, No. 2, 440--457 (2014; Zbl 1320.35046) Full Text: DOI
Rossi, Luca; Ryzhik, Lenya Transition waves for a class of space-time dependent monostable equations. (English) Zbl 1305.35092 Commun. Math. Sci. 12, No. 5, 879-900 (2014). MSC: 35K57 35C07 PDFBibTeX XMLCite \textit{L. Rossi} and \textit{L. Ryzhik}, Commun. Math. Sci. 12, No. 5, 879--900 (2014; Zbl 1305.35092) Full Text: DOI
Hamel, François; Ryzhik, Lenya On the nonlocal Fisher-KPP equation: steady states, spreading speed and global bounds. (English) Zbl 1317.35122 Nonlinearity 27, No. 11, 2735-2753 (2014). Reviewer: Josipa Pina Milišić (Zagreb) MSC: 35K57 35B10 PDFBibTeX XMLCite \textit{F. Hamel} and \textit{L. Ryzhik}, Nonlinearity 27, No. 11, 2735--2753 (2014; Zbl 1317.35122) Full Text: DOI arXiv
Ignatova, Mihaela; Kukavica, Igor; Ryzhik, Lenya The Harnack inequality for second-order elliptic equations with divergence-free drifts. (English) Zbl 1308.35039 Commun. Math. Sci. 12, No. 4, 681-694 (2014). Reviewer: Vincenzo Vespri (Firenze) MSC: 35B45 35B53 35B65 35J15 35Q35 PDFBibTeX XMLCite \textit{M. Ignatova} et al., Commun. Math. Sci. 12, No. 4, 681--694 (2014; Zbl 1308.35039) Full Text: DOI
Iyer, Gautam; Komorowski, Tomasz; Novikov, Alexei; Ryzhik, Lenya From homogenization to averaging in cellular flows. (English) Zbl 1302.35039 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31, No. 5, 957-983 (2014). MSC: 35B27 35P05 PDFBibTeX XMLCite \textit{G. Iyer} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 31, No. 5, 957--983 (2014; Zbl 1302.35039) Full Text: DOI arXiv
Komorowski, Tomasz; Ryzhik, Lenya Long time energy transfer in the random Schrödinger equation. (English) Zbl 1296.35110 Commun. Math. Phys. 329, No. 3, 1131-1170 (2014). Reviewer: Qin Meng Zhao (Beijing) MSC: 35Q20 35Q55 35Q41 82C31 35Q84 PDFBibTeX XMLCite \textit{T. Komorowski} and \textit{L. Ryzhik}, Commun. Math. Phys. 329, No. 3, 1131--1170 (2014; Zbl 1296.35110) Full Text: DOI
Berestycki, H.; Rodríguez, N.; Ryzhik, L. Traveling wave solutions in a reaction-diffusion model for criminal activity. (English) Zbl 1288.35160 Multiscale Model. Simul. 11, No. 4, 1097-1126 (2013). MSC: 35C07 35K57 35B08 35K45 35R09 PDFBibTeX XMLCite \textit{H. Berestycki} et al., Multiscale Model. Simul. 11, No. 4, 1097--1126 (2013; Zbl 1288.35160) Full Text: DOI arXiv
Komorowski, Tomasz; Olla, Stefano; Ryzhik, Lenya Asymptotics of the solutions of the stochastic lattice wave equation. (English) Zbl 1283.35143 Arch. Ration. Mech. Anal. 209, No. 2, 455-494 (2013). MSC: 35Q82 60H15 82C31 35B40 35R60 PDFBibTeX XMLCite \textit{T. Komorowski} et al., Arch. Ration. Mech. Anal. 209, No. 2, 455--494 (2013; Zbl 1283.35143) Full Text: DOI arXiv
Nadin, G.; Rossi, L.; Ryzhik, L.; Perthame, B. Wave-like solutions for nonlocal reaction-diffusion equations: a toy model. (English) Zbl 1280.34066 Math. Model. Nat. Phenom. 8, No. 3, 33-41 (2013). Reviewer: Panagiotis Ch. Tsamatos (Ioannina) MSC: 34K10 35B36 35C07 35K57 35R10 PDFBibTeX XMLCite \textit{G. Nadin} et al., Math. Model. Nat. Phenom. 8, No. 3, 33--41 (2013; Zbl 1280.34066) Full Text: DOI
Hamel, François; Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya A short proof of the logarithmic Bramson correction in Fisher-KPP equations. (English) Zbl 1275.35067 Netw. Heterog. Media 8, No. 1, 275-289 (2013). MSC: 35C07 35K57 35B40 PDFBibTeX XMLCite \textit{F. Hamel} et al., Netw. Heterog. Media 8, No. 1, 275--289 (2013; Zbl 1275.35067) Full Text: DOI
Kiselev, Alexander; Ryzhik, Lenya Biomixing by chemotaxis and efficiency of biological reactions: the critical reaction case. (English) Zbl 1300.92015 J. Math. Phys. 53, No. 11, 115609, 9 p. (2012). MSC: 92C17 35K35 35Q92 35K57 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{L. Ryzhik}, J. Math. Phys. 53, No. 11, 115609, 9 p. (2012; Zbl 1300.92015) Full Text: DOI arXiv
Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya; Zlatoš, Andrej Existence and non-existence of Fisher-KPP transition fronts. (English) Zbl 1267.35108 Arch. Ration. Mech. Anal. 203, No. 1, 217-246 (2012). Reviewer: Zhi-Cheng Wang (Lanzhou) MSC: 35K57 35Q92 35C07 PDFBibTeX XMLCite \textit{J. Nolen} et al., Arch. Ration. Mech. Anal. 203, No. 1, 217--246 (2012; Zbl 1267.35108) Full Text: DOI arXiv
Komorowski, Tomasz; Ryzhik, Lenya Fluctuations of solutions to Wigner equation with an Ornstein-Uhlenbeck potential. (English) Zbl 1244.82073 Discrete Contin. Dyn. Syst., Ser. B 17, No. 3, 871-914 (2012). MSC: 82C44 60H25 35Q40 82C70 PDFBibTeX XMLCite \textit{T. Komorowski} and \textit{L. Ryzhik}, Discrete Contin. Dyn. Syst., Ser. B 17, No. 3, 871--914 (2012; Zbl 1244.82073) Full Text: DOI
Kiselev, Alexander; Ryzhik, Lenya Biomixing by chemotaxis and enhancement of biological reactions. (English) Zbl 1236.35190 Commun. Partial Differ. Equations 37, No. 1-3, 298-318 (2012). MSC: 35Q92 92C17 35K35 35K57 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{L. Ryzhik}, Commun. Partial Differ. Equations 37, No. 1--3, 298--318 (2012; Zbl 1236.35190) Full Text: DOI arXiv
Bal, Guillaume; Komorowski, Tomasz; Ryzhik, Lenya Asymptotics of the solutions of the random Schrödinger equation. (English) Zbl 1231.35187 Arch. Ration. Mech. Anal. 200, No. 2, 613-664 (2011). Reviewer: Gabriel Stoltz (Marne-La-Vallée) MSC: 35Q41 60H15 35R60 PDFBibTeX XMLCite \textit{G. Bal} et al., Arch. Ration. Mech. Anal. 200, No. 2, 613--664 (2011; Zbl 1231.35187) Full Text: DOI
Komorowski, Tomasz; Ryzhik, Lenya A sharp bound on the \(L^2\) norm of the solution of a random elliptic difference equation. (English) Zbl 1222.39017 Commun. Math. Sci. 9, No. 2, 607-622 (2011). Reviewer: Grigori N. Milstein (Yekaterinburg) MSC: 39A50 35B27 60H25 PDFBibTeX XMLCite \textit{T. Komorowski} and \textit{L. Ryzhik}, Commun. Math. Sci. 9, No. 2, 607--622 (2011; Zbl 1222.39017) Full Text: DOI Euclid
Iyer, Gautam; Novikov, Alexei; Ryzhik, Lenya; Zlatoš, Andrej Exit times of diffusions with incompressible drift. (English) Zbl 1387.35493 SIAM J. Math. Anal. 42, No. 6, 2484-2498 (2010). MSC: 35Q35 76R50 35J25 35J60 35J05 35B40 PDFBibTeX XMLCite \textit{G. Iyer} et al., SIAM J. Math. Anal. 42, No. 6, 2484--2498 (2010; Zbl 1387.35493) Full Text: DOI arXiv
Bal, Guillaume; Komorowski, Tomasz; Ryzhik, Lenya Kinetic limits for waves in a random medium. (English) Zbl 1221.60095 Kinet. Relat. Models 3, No. 4, 529-644 (2010). Reviewer: Wolfgang Freudenberg (Cottbus) MSC: 60H25 35Q40 35Q41 35R60 82C40 PDFBibTeX XMLCite \textit{G. Bal} et al., Kinet. Relat. Models 3, No. 4, 529--644 (2010; Zbl 1221.60095) Full Text: DOI
Hamel, François; Ryzhik, Lenya Traveling fronts for the thermo-diffusive system with arbitrary Lewis numbers. (English) Zbl 1200.35044 Arch. Ration. Mech. Anal. 195, No. 3, 923-952 (2010). Reviewer: Vyacheslav I. Maksimov (Ekaterinburg) MSC: 35C07 35K57 76V05 35Q35 PDFBibTeX XMLCite \textit{F. Hamel} and \textit{L. Ryzhik}, Arch. Ration. Mech. Anal. 195, No. 3, 923--952 (2010; Zbl 1200.35044) Full Text: DOI
Berestycki, Henri; Kiselev, Alexander; Novikov, Alexei; Ryzhik, Lenya The explosion problem in a flow. (English) Zbl 1204.35131 J. Anal. Math. 110, 31-65 (2010). Reviewer: Luisa Consiglieri (Reguengo) MSC: 35Q35 35J60 35B09 35B30 76D03 PDFBibTeX XMLCite \textit{H. Berestycki} et al., J. Anal. Math. 110, 31--65 (2010; Zbl 1204.35131) Full Text: DOI arXiv
Komorowski, Tomasz; Peszat, Szymon; Ryzhik, Lenya Limit of fluctuations of solutions of Wigner equation. (English) Zbl 1179.81056 Commun. Math. Phys. 292, No. 2, 479-510 (2009). MSC: 81Q05 35R60 60H40 82C70 81S30 81S22 PDFBibTeX XMLCite \textit{T. Komorowski} et al., Commun. Math. Phys. 292, No. 2, 479--510 (2009; Zbl 1179.81056) Full Text: DOI
Berestycki, Henri; Nadin, Grégoire; Perthame, Benoit; Ryzhik, Lenya The non-local Fisher-KPP equation: travelling waves and steady states. (English) Zbl 1195.35088 Nonlinearity 22, No. 12, 2813-2844 (2009). Reviewer: Jens Rademacher (Amsterdam) MSC: 35C07 35K57 37N25 92D25 PDFBibTeX XMLCite \textit{H. Berestycki} et al., Nonlinearity 22, No. 12, 2813--2844 (2009; Zbl 1195.35088) Full Text: DOI
Mellet, Antoine; Nolen, James; Roquejoffre, Jean-Michel; Ryzhik, Lenya Stability of generalized transition fronts. (English) Zbl 1173.35021 Commun. Partial Differ. Equations 34, No. 6, 521-552 (2009). Reviewer: Michael I. Gil’ (Beer-Sheva) MSC: 35B35 35K57 35K15 35K55 PDFBibTeX XMLCite \textit{A. Mellet} et al., Commun. Partial Differ. Equations 34, No. 6, 521--552 (2009; Zbl 1173.35021) Full Text: DOI
Nolen, James; Ryzhik, Lenya Traveling waves in a one-dimensional heterogeneous medium. (English) Zbl 1178.35205 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 3, 1021-1047 (2009). MSC: 35K57 35K55 35K15 35B40 35R60 PDFBibTeX XMLCite \textit{J. Nolen} and \textit{L. Ryzhik}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 3, 1021--1047 (2009; Zbl 1178.35205) Full Text: DOI arXiv EuDML
Constantin, Peter; Kiselev, Alexander; Ryzhik, Lenya; Zlatoš, Andrej Diffusion and mixing in fluid flow. (English) Zbl 1180.35084 Ann. Math. (2) 168, No. 2, 643-674 (2008). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35B30 35K15 35K57 35Q35 58J35 PDFBibTeX XMLCite \textit{P. Constantin} et al., Ann. Math. (2) 168, No. 2, 643--674 (2008; Zbl 1180.35084) Full Text: DOI arXiv Link
Constantin, Peter; Novikov, Alexei; Ryzhik, Lenya Relaxation in reactive flows. (English) Zbl 1177.35119 Geom. Funct. Anal. 18, No. 4, 1145-1167 (2008). MSC: 35K57 35K15 35B40 35Q35 PDFBibTeX XMLCite \textit{P. Constantin} et al., Geom. Funct. Anal. 18, No. 4, 1145--1167 (2008; Zbl 1177.35119) Full Text: DOI
Nadin, Gregoire; Perthame, Benoît; Ryzhik, Lenya Traveling waves for the Keller-Segel system with Fisher birth terms. (English) Zbl 1154.35459 Interfaces Free Bound. 10, No. 4, 517-538 (2008). MSC: 35Q80 35K57 35B35 92C17 PDFBibTeX XMLCite \textit{G. Nadin} et al., Interfaces Free Bound. 10, No. 4, 517--538 (2008; Zbl 1154.35459) Full Text: DOI Link
Constantin, Peter; Roquejoffre, Jean-Michel; Ryzhik, Lenya; Vladimirova, Natalia Propagation and quenching in a reactive Burgers-Boussinesq system. (English) Zbl 1155.35085 Nonlinearity 21, No. 2, 221-271 (2008). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q53 35K57 35B40 76V05 35A35 80A25 PDFBibTeX XMLCite \textit{P. Constantin} et al., Nonlinearity 21, No. 2, 221--271 (2008; Zbl 1155.35085) Full Text: DOI
Papanicolaou, George; Ryzhik, Lenya; Sølna, Knut Self-averaging from lateral diversity in the Itô-Schrödinger equation. (English) Zbl 1143.35390 Multiscale Model. Simul. 6, No. 2, 468-492 (2007). MSC: 35R60 35Q55 60H15 74A40 74K10 PDFBibTeX XMLCite \textit{G. Papanicolaou} et al., Multiscale Model. Simul. 6, No. 2, 468--492 (2007; Zbl 1143.35390) Full Text: DOI
Ryzhik, Lenya; Zlatos, Andrej KPP pulsating front speed-up by flows. (English) Zbl 1152.35055 Commun. Math. Sci. 5, No. 3, 575-593 (2007). Reviewer: Bixiang Wang (Socorro) MSC: 35K57 35B05 PDFBibTeX XMLCite \textit{L. Ryzhik} and \textit{A. Zlatos}, Commun. Math. Sci. 5, No. 3, 575--593 (2007; Zbl 1152.35055) Full Text: DOI arXiv
Perthame, Benoît; Ryzhik, Lenya Moderate dispersion in conservation laws with convex fluxes. (English) Zbl 1141.35322 Commun. Math. Sci. 5, No. 2, 473-484 (2007). MSC: 35B25 35Q53 35L67 35L65 PDFBibTeX XMLCite \textit{B. Perthame} and \textit{L. Ryzhik}, Commun. Math. Sci. 5, No. 2, 473--484 (2007; Zbl 1141.35322) Full Text: DOI Euclid
Novikov, Alexei; Ryzhik, Lenya Boundary layers and KPP fronts in a cellular flow. (English) Zbl 1109.76064 Arch. Ration. Mech. Anal. 184, No. 1, 23-48 (2007). MSC: 76V05 35Q35 PDFBibTeX XMLCite \textit{A. Novikov} and \textit{L. Ryzhik}, Arch. Ration. Mech. Anal. 184, No. 1, 23--48 (2007; Zbl 1109.76064) Full Text: DOI
Constantin, Peter; Lewicka, Marta; Ryzhik, Lenya Travelling waves in two-dimensional reactive Boussinesq systems with no-slip boundary conditions. (English) Zbl 1106.76076 Nonlinearity 19, No. 11, 2605-2615 (2006). MSC: 76V05 35Q35 PDFBibTeX XMLCite \textit{P. Constantin} et al., Nonlinearity 19, No. 11, 2605--2615 (2006; Zbl 1106.76076) Full Text: DOI
Constantin, Peter; Domelevo, Komla; Roquejoffre, Jean-Michel; Ryzhik, Lenya Existence of pulsating waves in a model of flames in sprays. (English) Zbl 1110.35007 J. Eur. Math. Soc. (JEMS) 8, No. 4, 555-584 (2006). Reviewer: Jiaqi Mo (Wuhu) MSC: 35B25 80A25 PDFBibTeX XMLCite \textit{P. Constantin} et al., J. Eur. Math. Soc. (JEMS) 8, No. 4, 555--584 (2006; Zbl 1110.35007) Full Text: DOI
Berestycki, Henri; Constantin, Peter; Ryzhik, Lenya Non-planar fronts in Boussinesq reactive flows. (English) Zbl 1157.35469 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 4, 407-437 (2006). MSC: 35Q53 76D99 76V05 PDFBibTeX XMLCite \textit{H. Berestycki} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 23, No. 4, 407--437 (2006; Zbl 1157.35469) Full Text: DOI arXiv Numdam EuDML
Fannjiang, A.; Kiselev, A.; Ryzhik, L. Quenching of reaction by cellular flows. (English) Zbl 1097.35077 Geom. Funct. Anal. 16, No. 1, 40-69 (2006). Reviewer: Mohammed Bouchekif (Tlemcen) MSC: 35K57 35K15 35B40 35B05 PDFBibTeX XMLCite \textit{A. Fannjiang} et al., Geom. Funct. Anal. 16, No. 1, 40--69 (2006; Zbl 1097.35077) Full Text: DOI arXiv
Hamel, François; Ryzhik, Lenya Non-adiabatic KPP fronts with an arbitrary Lewis number. (English) Zbl 1083.35046 Nonlinearity 18, No. 6, 2881-2902 (2005). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35K57 35B45 35J60 35B05 76R50 80A25 PDFBibTeX XMLCite \textit{F. Hamel} and \textit{L. Ryzhik}, Nonlinearity 18, No. 6, 2881--2902 (2005; Zbl 1083.35046) Full Text: DOI Link
Berestycki, Henri; Hamel, Francois; Kiselev, Alexander; Ryzhik, Lenya Quenching and propagation in KPP reaction-diffusion equations with a heat loss. (English) Zbl 1087.35051 Arch. Ration. Mech. Anal. 178, No. 1, 57-80 (2005). Reviewer: Chiu Yeung Chan (Lafayette) MSC: 35K57 35B05 PDFBibTeX XMLCite \textit{H. Berestycki} et al., Arch. Ration. Mech. Anal. 178, No. 1, 57--80 (2005; Zbl 1087.35051) Full Text: DOI HAL
Novikov, Alexei; Papanicolaou, George; Ryzhik, Lenya Boundary layers for cellular flows at high Péclet numbers. (English) Zbl 1112.76023 Commun. Pure Appl. Math. 58, No. 7, 867-922 (2005). MSC: 76D10 35B25 35J25 PDFBibTeX XMLCite \textit{A. Novikov} et al., Commun. Pure Appl. Math. 58, No. 7, 867--922 (2005; Zbl 1112.76023) Full Text: DOI
Bal, Guillaume; Ryzhik, Lenya Stability of time reversed waves in changing media. (English) Zbl 1184.35187 Discrete Contin. Dyn. Syst. 12, No. 5, 793-815 (2005). MSC: 35L05 60H25 35Q40 PDFBibTeX XMLCite \textit{G. Bal} and \textit{L. Ryzhik}, Discrete Contin. Dyn. Syst. 12, No. 5, 793--815 (2005; Zbl 1184.35187) Full Text: DOI arXiv
Gordon, Peter V.; Ryzhik, Lenya; Vladimirova, Natalia The KPP system in a periodic flow with a heat loss. (English) Zbl 1117.80003 Nonlinearity 18, No. 2, 571-589 (2005). MSC: 80A25 35K57 PDFBibTeX XMLCite \textit{P. V. Gordon} et al., Nonlinearity 18, No. 2, 571--589 (2005; Zbl 1117.80003) Full Text: DOI
Perthame, Benoît; Ryzhik, Lenya Exponential decay for the fragmentation or cell-division equation. (English) Zbl 1072.35195 J. Differ. Equations 210, No. 1, 155-177 (2005). Reviewer: Michael I. Gil’ (Beer-Sheva) MSC: 35R10 92C37 35B35 35B40 PDFBibTeX XMLCite \textit{B. Perthame} and \textit{L. Ryzhik}, J. Differ. Equations 210, No. 1, 155--177 (2005; Zbl 1072.35195) Full Text: DOI
Perthame, Benoît; Ryzhik, Lenya The quantum scattering limit for a regularized Wigner equation. (English) Zbl 1092.81026 Methods Appl. Anal. 11, No. 3, 447-464 (2004). MSC: 81Q20 35B25 35B27 35Q40 82C40 81U05 PDFBibTeX XMLCite \textit{B. Perthame} and \textit{L. Ryzhik}, Methods Appl. Anal. 11, No. 3, 447--464 (2004; Zbl 1092.81026) Full Text: DOI
Bal, Guillaume; Ryzhik, Lenya Time splitting for the Liouville equation in a random medium. (English) Zbl 1082.65093 Commun. Math. Sci. 2, No. 3, 515-534 (2004). MSC: 65M20 65M12 60F05 60H15 35L60 65C30 PDFBibTeX XMLCite \textit{G. Bal} and \textit{L. Ryzhik}, Commun. Math. Sci. 2, No. 3, 515--534 (2004; Zbl 1082.65093) Full Text: DOI
Bal, Guillaume; Ryzhik, Lenya Time splitting for wave equations in random media. (English) Zbl 1130.74393 M2AN, Math. Model. Numer. Anal. 38, No. 6, 961-987 (2004). MSC: 74J20 35L05 65M06 74E05 74E30 74H15 PDFBibTeX XMLCite \textit{G. Bal} and \textit{L. Ryzhik}, M2AN, Math. Model. Numer. Anal. 38, No. 6, 961--987 (2004; Zbl 1130.74393) Full Text: DOI Numdam EuDML
Papanicolaou, George; Ryzhik, Leonid; Solna, Knut Statistical stability in time reversal. (English) Zbl 1065.35058 SIAM J. Appl. Math. 64, No. 4, 1133-1155 (2004). Reviewer: Yana Belopolskaya (St. Petersburg) MSC: 35B35 60H15 35Q60 PDFBibTeX XMLCite \textit{G. Papanicolaou} et al., SIAM J. Appl. Math. 64, No. 4, 1133--1155 (2004; Zbl 1065.35058) Full Text: DOI arXiv
Bal, Guillaume; Komorowski, Tomasz; Ryzhik, Lenya Self-averaging of Wigner transforms in random media. (English) Zbl 1037.35108 Commun. Math. Phys. 242, No. 1-2, 81-135 (2003). MSC: 35R60 60H15 81S30 PDFBibTeX XMLCite \textit{G. Bal} et al., Commun. Math. Phys. 242, No. 1--2, 81--135 (2003; Zbl 1037.35108) Full Text: DOI arXiv
Constantin, Peter; Kiselev, Alexander; Ryzhik, Lenya Fronts in reactive convection: Bounds, stability, and instability. (English) Zbl 1072.76068 Commun. Pure Appl. Math. 56, No. 12, 1781-1803 (2003). MSC: 76V05 76E06 35Q35 80A25 76E30 PDFBibTeX XMLCite \textit{P. Constantin} et al., Commun. Pure Appl. Math. 56, No. 12, 1781--1803 (2003; Zbl 1072.76068) Full Text: DOI arXiv
Bal, Guillaume; Ryzhik, Leonid Time reversal and refocusing in random media. (English) Zbl 1126.76360 SIAM J. Appl. Math. 63, No. 5, 1475-1498 (2003). MSC: 76Q05 35B40 35Q35 35F10 74J05 78A40 82D30 PDFBibTeX XMLCite \textit{G. Bal} and \textit{L. Ryzhik}, SIAM J. Appl. Math. 63, No. 5, 1475--1498 (2003; Zbl 1126.76360) Full Text: DOI arXiv
Mischler, Stéphane; Perthame, Benoît; Ryzhik, Lenya Stability in a nonlinear population maturation model. (English) Zbl 1020.92025 Math. Models Methods Appl. Sci. 12, No. 12, 1751-1772 (2002). Reviewer: Svitlana P.Rogovchenko (Famagusta) MSC: 92D25 35Q92 35F30 PDFBibTeX XMLCite \textit{S. Mischler} et al., Math. Models Methods Appl. Sci. 12, No. 12, 1751--1772 (2002; Zbl 1020.92025) Full Text: DOI
Bal, Guillaume; Papanicolaou, George; Ryzhik, Leonid Self-averaging in time reversal for the parabolic wave equation. (English) Zbl 1020.35126 Stoch. Dyn. 2, No. 4, 507-531 (2002). Reviewer: Messoud Efendiev (Berlin) MSC: 35R60 35Q40 60H25 PDFBibTeX XMLCite \textit{G. Bal} et al., Stoch. Dyn. 2, No. 4, 507--531 (2002; Zbl 1020.35126) Full Text: DOI arXiv
Bal, Guillaume; Papanicolaou, George; Ryzhik, Leonid Radiative transport limit for the random Schrödinger equation. (English) Zbl 0999.60061 Nonlinearity 15, No. 2, 513-529 (2002). Reviewer: Stanislaw Wedrychowicz (Rzeszów) MSC: 60H15 35R60 PDFBibTeX XMLCite \textit{G. Bal} et al., Nonlinearity 15, No. 2, 513--529 (2002; Zbl 0999.60061) Full Text: DOI arXiv
Constantin, Peter; Kiselev, Alexander; Ryzhik, Leonid Quenching of flames by fluid advection. (English) Zbl 1032.35087 Commun. Pure Appl. Math. 54, No. 11, 1320-1342 (2001). Reviewer: Ning Su (Beijing) MSC: 35K57 35B40 35B05 80A25 PDFBibTeX XMLCite \textit{P. Constantin} et al., Commun. Pure Appl. Math. 54, No. 11, 1320--1342 (2001; Zbl 1032.35087) Full Text: DOI arXiv
Kiselev, Alexander; Ryzhik, Leonid An upper bound for the bulk burning rate for systems. (English) Zbl 0988.35080 Nonlinearity 14, No. 5, 1297-1310 (2001). Reviewer: Lubomira Softova (Bari) MSC: 35K57 35K45 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{L. Ryzhik}, Nonlinearity 14, No. 5, 1297--1310 (2001; Zbl 0988.35080) Full Text: DOI arXiv
Kiselev, Alexander; Ryzhik, Leonid Enhancement of the traveling front speeds in reaction-diffusion equations with advection. (English) Zbl 1002.35069 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 3, 309-358 (2001). Reviewer: Messoud Efendiev (Berlin) MSC: 35K57 80A32 35K40 35B45 35B10 PDFBibTeX XMLCite \textit{A. Kiselev} and \textit{L. Ryzhik}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 18, No. 3, 309--358 (2001; Zbl 1002.35069) Full Text: DOI arXiv Numdam EuDML
Constantin, Peter; Kiselev, Alexander; Oberman, Adam; Ryzhik, Leonid Bulk burning rate in passive-reactive diffusion. (English) Zbl 0979.76093 Arch. Ration. Mech. Anal. 154, No. 1, 53-91 (2000). Reviewer: Dian K.Palagachev (Bari) MSC: 76V05 35K57 92E20 PDFBibTeX XMLCite \textit{P. Constantin} et al., Arch. Ration. Mech. Anal. 154, No. 1, 53--91 (2000; Zbl 0979.76093) Full Text: DOI arXiv
Bal, Guillaume; Papanicolaou, George; Ryzhik, Leonid Diffusive energy scattering from weakly random surfaces. (English) Zbl 0967.76084 J. Math. Phys. 40, No. 10, 4813-4827 (1999). MSC: 76Q05 35P25 PDFBibTeX XMLCite \textit{G. Bal} et al., J. Math. Phys. 40, No. 10, 4813--4827 (1999; Zbl 0967.76084) Full Text: DOI Link
Bal, Guillaume; Fannjiang, Albert; Papanicolaou, George; Ryzhik, Leonid Radiative transport in a periodic structure. (English) Zbl 0964.82048 J. Stat. Phys. 95, No. 1-2, 479-494 (1999). MSC: 82C70 35R60 35Q99 74Q10 74A40 74E05 PDFBibTeX XMLCite \textit{G. Bal} et al., J. Stat. Phys. 95, No. 1--2, 479--494 (1999; Zbl 0964.82048) Full Text: DOI arXiv
Papanicolaou, George; Ryzhik, Leonid Waves and transport. (English) Zbl 0930.35172 Caffarelli, Luis (ed.) et al., Hyperbolic equations and frequency interactions. Providence, RI: American Mathematical Society. IAS/ Park City Math. Ser. 5, 305-382 (1999). Reviewer: T.Aktosun (Fargo) MSC: 35Q72 35-02 76Q05 78A48 74H50 82D30 PDFBibTeX XMLCite \textit{G. Papanicolaou} and \textit{L. Ryzhik}, in: Hyperbolic equations and frequency interactions. Providence, RI: American Mathematical Society. 305--382 (1999; Zbl 0930.35172)
Ryzhik, Leonid; Papanicolaou, George C.; Keller, Joseph B. Transport equations for waves in a half space. (English) Zbl 0895.35010 Commun. Partial Differ. Equations 22, No. 11-12, 1869-1910 (1997). MSC: 35B27 35L65 76Q05 PDFBibTeX XMLCite \textit{L. Ryzhik} et al., Commun. Partial Differ. Equations 22, No. 11--12, 1869--1910 (1997; Zbl 0895.35010)
Ryzhik, L. V.; Shul’man, E. I. Symmetry algebra of nonlinear integrable equations. (English. Russian original) Zbl 0852.35129 Theor. Math. Phys. 94, No. 4, 387-392 (1993); translation from Teor. Mat. Fiz. 95, No. 1, 34-41 (1993). MSC: 35Q53 58J70 81U40 PDFBibTeX XMLCite \textit{L. V. Ryzhik} and \textit{E. I. Shul'man}, Theor. Math. Phys. 94, No. 4, 387--392 (1993; Zbl 0852.35129); translation from Teor. Mat. Fiz. 95, No. 1, 34--41 (1993) Full Text: DOI