Li, Liang; Shen, Ruipeng; Wei, Lijuan Explicit formula of radiation fields of free waves with applications on channel of energy. (English) Zbl 07818642 Anal. PDE 17, No. 2, 723-748 (2024). MSC: 35L05 PDFBibTeX XMLCite \textit{L. Li} et al., Anal. PDE 17, No. 2, 723--748 (2024; Zbl 07818642) Full Text: DOI arXiv
Dodson, Benjamin Spacetime integral bounds for the energy-critical nonlinear wave equation. (English) Zbl 07805271 Proc. Am. Math. Soc. 152, No. 3, 1169-1180 (2024). MSC: 35Q55 35B25 35R09 35A01 35A02 PDFBibTeX XMLCite \textit{B. Dodson}, Proc. Am. Math. Soc. 152, No. 3, 1169--1180 (2024; Zbl 07805271) Full Text: DOI arXiv
Dodson, Benjamin Global well-posedness for the radial, defocusing, nonlinear wave equation for \(3 < p < 5\). (English) Zbl 07791557 Am. J. Math. 146, No. 1, 1-46 (2024). Reviewer: Chengbo Wang (Hangzhou) MSC: 35L71 35L15 35L05 35B40 PDFBibTeX XMLCite \textit{B. Dodson}, Am. J. Math. 146, No. 1, 1--46 (2024; Zbl 07791557) Full Text: DOI arXiv
Li, Liang; Shen, Ruipeng; Wei, Lijuan Energy distribution of solutions to defocusing semi-linear wave equation in two dimensional space. (English) Zbl 1518.35498 Math. Ann. 386, No. 3-4, 1267-1303 (2023). MSC: 35L71 35B40 35L15 PDFBibTeX XMLCite \textit{L. Li} et al., Math. Ann. 386, No. 3--4, 1267--1303 (2023; Zbl 1518.35498) Full Text: DOI arXiv
Spitz, Martin On the almost sure scattering for the energy-critical cubic wave equation with supercritical data. (English) Zbl 1502.35025 Commun. Pure Appl. Anal. 21, No. 12, 4041-4070 (2022). MSC: 35B40 35L15 35L71 35R60 PDFBibTeX XMLCite \textit{M. Spitz}, Commun. Pure Appl. Anal. 21, No. 12, 4041--4070 (2022; Zbl 1502.35025) Full Text: DOI arXiv
Sá Barreto, Antônio; Uhlmann, Gunther; Wang, Yiran Inverse scattering for critical semilinear wave equations. (English) Zbl 1500.35220 Pure Appl. Anal. 4, No. 2, 191-223 (2022). MSC: 35P25 35J15 35J61 35R30 58J50 PDFBibTeX XMLCite \textit{A. Sá Barreto} et al., Pure Appl. Anal. 4, No. 2, 191--223 (2022; Zbl 1500.35220) Full Text: DOI arXiv
Singh, Soniya; Arora, Sumit; Mohan, Manil T.; Dabas, Jaydev Approximate controllability of second order impulsive systems with state-dependent delay in Banach spaces. (English) Zbl 1483.34106 Evol. Equ. Control Theory 11, No. 1, 67-93 (2022). MSC: 34K30 34K43 34K45 93B05 PDFBibTeX XMLCite \textit{S. Singh} et al., Evol. Equ. Control Theory 11, No. 1, 67--93 (2022; Zbl 1483.34106) Full Text: DOI
Duyckaerts, Thomas; Kenig, Carlos; Martel, Yvan; Merle, Frank Soliton resolution for critical co-rotational wave maps and radial cubic wave equation. (English) Zbl 1491.35292 Commun. Math. Phys. 391, No. 2, 779-871 (2022). Reviewer: Dongbing Zha (Shanghai) MSC: 35L71 35B40 35B44 35L15 35Q55 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., Commun. Math. Phys. 391, No. 2, 779--871 (2022; Zbl 1491.35292) Full Text: DOI arXiv
Dodson, Benjamin Scattering for the radial defocusing cubic nonlinear wave equation with initial data in the critical Sobolev space. (English) Zbl 1479.35549 Duke Math. J. 170, No. 15, 3267-3321 (2021). MSC: 35L15 35L71 35P25 PDFBibTeX XMLCite \textit{B. Dodson}, Duke Math. J. 170, No. 15, 3267--3321 (2021; Zbl 1479.35549) Full Text: DOI
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank Decay estimates for nonradiative solutions of the energy-critical focusing wave equation. (English) Zbl 1472.35050 J. Geom. Anal. 31, No. 7, 7036-7074 (2021). MSC: 35B40 35C08 35L15 35L71 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Geom. Anal. 31, No. 7, 7036--7074 (2021; Zbl 1472.35050) Full Text: DOI arXiv
Beckner, William Symmetry in Fourier analysis: Heisenberg group to Stein-Weiss integrals. (English) Zbl 1471.42018 J. Geom. Anal. 31, No. 7, 7008-7035 (2021). MSC: 42B10 35A15 58J70 PDFBibTeX XMLCite \textit{W. Beckner}, J. Geom. Anal. 31, No. 7, 7008--7035 (2021; Zbl 1471.42018) Full Text: DOI
Looi, Shi-Zhuo; Tohaneanu, Mihai Scattering for critical wave equations with variable coefficients. (English) Zbl 1467.35230 Proc. Edinb. Math. Soc., II. Ser. 64, No. 2, 298-316 (2021). MSC: 35P25 35L15 35L71 PDFBibTeX XMLCite \textit{S.-Z. Looi} and \textit{M. Tohaneanu}, Proc. Edinb. Math. Soc., II. Ser. 64, No. 2, 298--316 (2021; Zbl 1467.35230) Full Text: DOI arXiv
Shen, Ruipeng Inward/outward energy theory of non-radial solutions to 3D semi-linear wave equation. (English) Zbl 1450.35175 Adv. Math. 374, Article ID 107384, 46 p. (2020). MSC: 35L71 35L15 PDFBibTeX XMLCite \textit{R. Shen}, Adv. Math. 374, Article ID 107384, 46 p. (2020; Zbl 1450.35175) Full Text: DOI arXiv
Mokdad, Mokdad Decay of Maxwell fields on Reissner-Nordström-de Sitter black holes. (English) Zbl 1442.35451 Lett. Math. Phys. 110, No. 7, 1961-2018 (2020). MSC: 35Q75 83C57 83C22 83C30 PDFBibTeX XMLCite \textit{M. Mokdad}, Lett. Math. Phys. 110, No. 7, 1961--2018 (2020; Zbl 1442.35451) Full Text: DOI arXiv
Inui, Takahisa; Kishimoto, Nobu; Nishimura, Kuranosuke Blow-up of the radially symmetric solutions for the quadratic nonlinear Schrödinger system without mass-resonance. (English) Zbl 1470.35334 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 198, Article ID 111895, 9 p. (2020). Reviewer: Zhiyong Wang (Fuzhou) MSC: 35Q55 35Q41 35B44 35B34 35B06 PDFBibTeX XMLCite \textit{T. Inui} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 198, Article ID 111895, 9 p. (2020; Zbl 1470.35334) Full Text: DOI arXiv
Jendrej, Jacek; Martel, Yvan Construction of multi-bubble solutions for the energy-critical wave equation in dimension 5. (English. French summary) Zbl 1471.35205 J. Math. Pures Appl. (9) 139, 317-355 (2020). Reviewer: Shuangjie Peng (Wuhan) MSC: 35L71 35B44 35B40 35L15 PDFBibTeX XMLCite \textit{J. Jendrej} and \textit{Y. Martel}, J. Math. Pures Appl. (9) 139, 317--355 (2020; Zbl 1471.35205) Full Text: DOI arXiv
Shen, Ruipeng Bounded solutions to an energy subcritical non-linear wave equation on \(\mathbb{R}^3\). (English) Zbl 1439.35340 J. Differ. Equations 269, No. 4, 3943-3986 (2020). MSC: 35L71 35L15 35B40 PDFBibTeX XMLCite \textit{R. Shen}, J. Differ. Equations 269, No. 4, 3943--3986 (2020; Zbl 1439.35340) Full Text: DOI arXiv
Azaiez, Asma Refined regularity for the blow-up set at non characteristic points for the vector-valued semilinear wave equation. (English) Zbl 1481.35080 Commun. Pure Appl. Anal. 18, No. 5, 2397-2408 (2019). MSC: 35B44 35B53 35B65 35L52 35L71 58J45 PDFBibTeX XMLCite \textit{A. Azaiez}, Commun. Pure Appl. Anal. 18, No. 5, 2397--2408 (2019; Zbl 1481.35080) Full Text: DOI arXiv
Inui, Takahisa The Strichartz estimates for the damped wave equation and the behavior of solutions for the energy critical nonlinear equation. (English) Zbl 1435.35253 NoDEA, Nonlinear Differ. Equ. Appl. 26, No. 6, Paper No. 50, 30 p. (2019). Reviewer: Alessandro Selvitella (Fort Wayne) MSC: 35L71 35A01 35B40 35B44 35B45 PDFBibTeX XMLCite \textit{T. Inui}, NoDEA, Nonlinear Differ. Equ. Appl. 26, No. 6, Paper No. 50, 30 p. (2019; Zbl 1435.35253) Full Text: DOI arXiv
Cazenave, Thierry; Martel, Yvan; Zhao, Lifeng Solutions with prescribed local blow-up surface for the nonlinear wave equation. (English) Zbl 1437.35494 Adv. Nonlinear Stud. 19, No. 4, 639-675 (2019). MSC: 35L71 35L15 35B44 35B40 PDFBibTeX XMLCite \textit{T. Cazenave} et al., Adv. Nonlinear Stud. 19, No. 4, 639--675 (2019; Zbl 1437.35494) Full Text: DOI arXiv
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank Scattering profile for global solutions of the energy-critical wave equation. (English) Zbl 1437.35497 J. Eur. Math. Soc. (JEMS) 21, No. 7, 2117-2162 (2019). MSC: 35L71 35L15 35B33 35B40 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Eur. Math. Soc. (JEMS) 21, No. 7, 2117--2162 (2019; Zbl 1437.35497) Full Text: DOI arXiv
Dodson, Benjamin Global well-posedness and scattering for the radial, defocusing, cubic wave equation with initial data in a critical Besov space. (English) Zbl 1403.35145 Anal. PDE 12, No. 4, 1023-1048 (2019). MSC: 35L05 35B40 PDFBibTeX XMLCite \textit{B. Dodson}, Anal. PDE 12, No. 4, 1023--1048 (2019; Zbl 1403.35145) Full Text: DOI arXiv
Tarulli, Mirko Well-posedness for nonlinear wave equation with potentials vanishing at infinity. (English) Zbl 1432.35143 J. Fourier Anal. Appl. 24, No. 4, 1000-1036 (2018). Reviewer: Chengbo Wang (Hangzhou) MSC: 35L71 42B20 42B25 PDFBibTeX XMLCite \textit{M. Tarulli}, J. Fourier Anal. Appl. 24, No. 4, 1000--1036 (2018; Zbl 1432.35143) Full Text: DOI
Duyckaerts, Thomas; Yang, Jianwei Blow-up of a critical Sobolev norm for energy-subcritical and energy-supercritical wave equations. (English) Zbl 1395.35043 Anal. PDE 11, No. 4, 983-1028 (2018). Reviewer: Dongbing Zha (Shanghai) MSC: 35B44 35L71 35B40 PDFBibTeX XMLCite \textit{T. Duyckaerts} and \textit{J. Yang}, Anal. PDE 11, No. 4, 983--1028 (2018; Zbl 1395.35043) Full Text: DOI arXiv
Pocovnicu, Oana Almost sure global well-posedness for the energy-critical defocusing nonlinear wave equation on \(\mathbb R^d\), \(d=4\) and \(5\). (English) Zbl 1375.35278 J. Eur. Math. Soc. (JEMS) 19, No. 8, 2521-2575 (2017). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L71 35R60 35L15 PDFBibTeX XMLCite \textit{O. Pocovnicu}, J. Eur. Math. Soc. (JEMS) 19, No. 8, 2521--2575 (2017; Zbl 1375.35278) Full Text: DOI arXiv
Azaiez, Asma; Zaag, Hatem A modulation technique for the blow-up profile of the vector-valued semilinear wave equation. (English) Zbl 1387.35065 Bull. Sci. Math. 141, No. 4, 312-352 (2017). MSC: 35B44 35L71 PDFBibTeX XMLCite \textit{A. Azaiez} and \textit{H. Zaag}, Bull. Sci. Math. 141, No. 4, 312--352 (2017; Zbl 1387.35065) Full Text: DOI arXiv
Jendrej, Jacek Construction of two-bubble solutions for some energy-critical wave equations. (English) Zbl 1357.35227 Sémin. Laurent Schwartz, EDP Appl. 2015-2016, Exp. No. 21, 10 p. (2016). MSC: 35L71 PDFBibTeX XMLCite \textit{J. Jendrej}, Sémin. Laurent Schwartz, EDP Appl. 2015--2016, Exp. No. 21, 10 p. (2016; Zbl 1357.35227) Full Text: DOI Numdam
Martel, Yvan; Merle, Frank Construction of multi-solitons for the energy-critical wave equation in dimension 5. (English) Zbl 1359.35166 Arch. Ration. Mech. Anal. 222, No. 3, 1113-1160 (2016). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q51 35C08 35C07 PDFBibTeX XMLCite \textit{Y. Martel} and \textit{F. Merle}, Arch. Ration. Mech. Anal. 222, No. 3, 1113--1160 (2016; Zbl 1359.35166) Full Text: DOI arXiv
Shen, Ruipeng; Staffilani, Gigliola A semi-linear shifted wave equation on the hyperbolic spaces with application on a quintic wave equation on \(\mathbb R^2\). (English) Zbl 1339.35190 Trans. Am. Math. Soc. 368, No. 4, 2809-2864 (2016). MSC: 35L71 35P25 PDFBibTeX XMLCite \textit{R. Shen} and \textit{G. Staffilani}, Trans. Am. Math. Soc. 368, No. 4, 2809--2864 (2016; Zbl 1339.35190) Full Text: DOI arXiv
Oh, Tadahiro; Pocovnicu, Oana Probabilistic global well-posedness of the energy-critical defocusing quintic nonlinear wave equation on \(\mathbb R^3\). (English. French summary) Zbl 1343.35167 J. Math. Pures Appl. (9) 105, No. 3, 342-366 (2016). MSC: 35L71 35L15 35R60 PDFBibTeX XMLCite \textit{T. Oh} and \textit{O. Pocovnicu}, J. Math. Pures Appl. (9) 105, No. 3, 342--366 (2016; Zbl 1343.35167) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Dynamics near explicit stationary solutions in similarity variables for solutions of a semilinear wave equation in higher dimensions. (English) Zbl 1339.35062 Trans. Am. Math. Soc. 368, No. 1, 27-87 (2016). MSC: 35B44 35L71 35L67 35B40 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Trans. Am. Math. Soc. 368, No. 1, 27--87 (2016; Zbl 1339.35062) Full Text: DOI arXiv
Zhu, Shihui Sharp energy criteria of blow-up for the energy-critical Klein-Gordon equation. (English) Zbl 1327.35330 J. Inequal. Appl. 2015, Paper No. 383, 9 p. (2015). MSC: 35Q40 35L05 PDFBibTeX XMLCite \textit{S. Zhu}, J. Inequal. Appl. 2015, Paper No. 383, 9 p. (2015; Zbl 1327.35330) Full Text: DOI
Jia, Hao; Liu, Baoping; Xu, Guixiang Long time dynamics of defocusing energy critical \(3+1\) dimensional wave equation with potential in the radial case. (English) Zbl 1329.35208 Commun. Math. Phys. 339, No. 2, 353-384 (2015). MSC: 35L71 35L15 35B40 35B07 PDFBibTeX XMLCite \textit{H. Jia} et al., Commun. Math. Phys. 339, No. 2, 353--384 (2015; Zbl 1329.35208) Full Text: DOI arXiv
Azaiez, Asma Blow-up profile for the complex-valued semilinear wave equation. (English) Zbl 1316.35200 Trans. Am. Math. Soc. 367, No. 8, 5891-5933 (2015). MSC: 35L71 35L81 35B44 39B32 35B40 35B35 PDFBibTeX XMLCite \textit{A. Azaiez}, Trans. Am. Math. Soc. 367, No. 8, 5891--5933 (2015; Zbl 1316.35200) Full Text: DOI arXiv
Todorova, Grozdena; Yordanov, Borislav On the regularizing effect of nonlinear damping in hyperbolic equations. (English) Zbl 1315.35049 Trans. Am. Math. Soc. 367, No. 7, 5043-5058 (2015). MSC: 35B65 35B33 35L71 PDFBibTeX XMLCite \textit{G. Todorova} and \textit{B. Yordanov}, Trans. Am. Math. Soc. 367, No. 7, 5043--5058 (2015; Zbl 1315.35049) Full Text: DOI
Saanouni, Tarek A blowing up wave equation with exponential type nonlinearity and arbitrary positive energy. (English) Zbl 1297.35055 J. Math. Anal. Appl. 421, No. 1, 444-452 (2015). MSC: 35B44 35L71 35L20 PDFBibTeX XMLCite \textit{T. Saanouni}, J. Math. Anal. Appl. 421, No. 1, 444--452 (2015; Zbl 1297.35055) Full Text: DOI
Guo, Zihua; Wang, Yuzhao Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations. (English) Zbl 1308.35271 J. Anal. Math. 124, 1-38 (2014). MSC: 35Q55 35L05 35B45 35R11 PDFBibTeX XMLCite \textit{Z. Guo} and \textit{Y. Wang}, J. Anal. Math. 124, 1--38 (2014; Zbl 1308.35271) Full Text: DOI arXiv
Beceanu, Marius A center-stable manifold for the energy-critical wave equation in \(\mathbb{R}^{3}\) in the symmetric setting. (English) Zbl 1315.35129 J. Hyperbolic Differ. Equ. 11, No. 3, 437-476 (2014). Reviewer: Chengbo Wang (Hangzhou) MSC: 35L71 35B44 35C08 37K40 35B40 PDFBibTeX XMLCite \textit{M. Beceanu}, J. Hyperbolic Differ. Equ. 11, No. 3, 437--476 (2014; Zbl 1315.35129) Full Text: DOI arXiv
Franchi, Bruno; Obrecht, Enrico; Vecchi, Eugenio On a class of semilinear evolution equations for vector potentials associated with Maxwell’s equations in Carnot groups. (English) Zbl 1284.35420 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 90, 56-69 (2013). MSC: 35Q61 35R03 58A10 49J45 22E25 PDFBibTeX XMLCite \textit{B. Franchi} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 90, 56--69 (2013; Zbl 1284.35420) Full Text: DOI
Wang, Dawei Global well-posedness and scattering for the nonstandard defocusing beam equation. (English) Zbl 1282.35108 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 89, 8-23 (2013). MSC: 35B45 47J35 35L76 74K10 35L30 PDFBibTeX XMLCite \textit{D. Wang}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 89, 8--23 (2013; Zbl 1282.35108) Full Text: DOI
Côte, Raphaël; Zaag, Hatem Construction of a multisoliton blowup solution to the semilinear wave equation in one space dimension. (English) Zbl 1295.35124 Commun. Pure Appl. Math. 66, No. 10, 1541-1581 (2013). Reviewer: Yvan Martel (Palaiseau) MSC: 35B44 35L71 35B40 37K40 35C08 PDFBibTeX XMLCite \textit{R. Côte} and \textit{H. Zaag}, Commun. Pure Appl. Math. 66, No. 10, 1541--1581 (2013; Zbl 1295.35124) Full Text: DOI arXiv
Saanouni, T. Blowing-up semilinear wave equation with exponential nonlinearity in two space dimensions. (English) Zbl 1275.35051 Proc. Indian Acad. Sci., Math. Sci. 123, No. 3, 365-372 (2013). MSC: 35B44 35L71 35L15 PDFBibTeX XMLCite \textit{T. Saanouni}, Proc. Indian Acad. Sci., Math. Sci. 123, No. 3, 365--372 (2013; Zbl 1275.35051) Full Text: DOI
Donninger, Roland; Krieger, Joachim Nonscattering solutions and blowup at infinity for the critical wave equation. (English) Zbl 1280.35135 Math. Ann. 357, No. 1, 89-163 (2013). Reviewer: Xingbin Pan (Shanghai) MSC: 35Q55 35L05 35B33 35B40 35B44 PDFBibTeX XMLCite \textit{R. Donninger} and \textit{J. Krieger}, Math. Ann. 357, No. 1, 89--163 (2013; Zbl 1280.35135) Full Text: DOI arXiv
Bulut, Aynur; Czubak, Magdalena; Li, Dong; Pavlović, Nataša; Zhang, Xiaoyi Stability and unconditional uniqueness of solutions for energy critical wave equations in high dimensions. (English) Zbl 1332.35007 Commun. Partial Differ. Equations 38, No. 4-6, 575-607 (2013). Reviewer: Jean-Marc Bouclet (Toulouse) MSC: 35A02 35L71 35B35 PDFBibTeX XMLCite \textit{A. Bulut} et al., Commun. Partial Differ. Equations 38, No. 4--6, 575--607 (2013; Zbl 1332.35007) Full Text: DOI arXiv
Kenig, Carlos E. The concentration-compactness rigidity method for critical dispersive and wave equations. (English) Zbl 1284.35289 Cabré, Xavier (ed.) et al., Nonlinear partial differential equations. Lecture notes from the school on topics in PDE’s and applications, Granada and Barcelona, Spain, 2008. Basel: Birkhäuser (ISBN 978-3-0348-0190-4/pbk; 978-3-0348-0191-1/ebook). Advanced Courses in Mathematics - CRM Barcelona, 117-149 (2012). Reviewer: Satyanad Kichenassamy (Reims) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{C. E. Kenig}, in: Nonlinear partial differential equations. Lecture notes from the school on topics in PDE's and applications, Granada and Barcelona, Spain, 2008. Basel: Birkhäuser. 117--149 (2012; Zbl 1284.35289) Full Text: DOI
Merle, Frank; Zaag, Hatem Isolatedness of characteristic points at blowup for a 1-dimensional semilinear wave equation. (English) Zbl 1270.35320 Duke Math. J. 161, No. 15, 2837-2908 (2012). Reviewer: Satyanad Kichenassamy (Reims) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Duke Math. J. 161, No. 15, 2837--2908 (2012; Zbl 1270.35320) Full Text: DOI arXiv Euclid
Duyckaerts, Thomas; Kenig, Carlos E.; Merle, Frank Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case. (English) Zbl 1282.35088 J. Eur. Math. Soc. (JEMS) 14, No. 5, 1389-1454 (2012). Reviewer: Marcelo M. Cavalcanti (Maringá) MSC: 35B44 35L71 35B33 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Eur. Math. Soc. (JEMS) 14, No. 5, 1389--1454 (2012; Zbl 1282.35088) Full Text: DOI arXiv
Bulut, Aynur Global well-posedness and scattering for the defocusing energy-supercritical cubic nonlinear wave equation. (English) Zbl 1258.35147 J. Funct. Anal. 263, No. 6, 1609-1660 (2012). Reviewer: Svetlin Georgiev (Rousse) MSC: 35L71 35L15 PDFBibTeX XMLCite \textit{A. Bulut}, J. Funct. Anal. 263, No. 6, 1609--1660 (2012; Zbl 1258.35147) Full Text: DOI arXiv
Killip, Rowan; Visan, Monica The defocusing energy-supercritical nonlinear wave equation in three space dimensions. (English) Zbl 1230.35068 Trans. Am. Math. Soc. 363, No. 7, 3893-3934 (2011). Reviewer: Satyanad Kichenassamy (Reims) MSC: 35L71 35L15 35B45 35B40 PDFBibTeX XMLCite \textit{R. Killip} and \textit{M. Visan}, Trans. Am. Math. Soc. 363, No. 7, 3893--3934 (2011; Zbl 1230.35068) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Blow-up behavior outside the origin for a semilinear wave equation in the radial case. (English) Zbl 1222.35126 Bull. Sci. Math. 135, No. 4, 353-373 (2011). Reviewer: Marie Kopáčková (Praha) MSC: 35L71 35L05 35B44 35B40 35L67 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Bull. Sci. Math. 135, No. 4, 353--373 (2011; Zbl 1222.35126) Full Text: DOI arXiv
Killip, Rowan; Visan, Monica The radial defocusing energy-supercritical nonlinear wave equation in all space dimensions. (English) Zbl 1218.35148 Proc. Am. Math. Soc. 139, No. 5, 1805-1817 (2011). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L71 35L15 35B44 PDFBibTeX XMLCite \textit{R. Killip} and \textit{M. Visan}, Proc. Am. Math. Soc. 139, No. 5, 1805--1817 (2011; Zbl 1218.35148) Full Text: DOI arXiv
Duyckaerts, Thomas; Kenig, Carlos; Merle, Frank Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation. (English) Zbl 1230.35067 J. Eur. Math. Soc. (JEMS) 13, No. 3, 533-599 (2011). Reviewer: Pavol Quittner (Bratislava) MSC: 35L71 35B44 PDFBibTeX XMLCite \textit{T. Duyckaerts} et al., J. Eur. Math. Soc. (JEMS) 13, No. 3, 533--599 (2011; Zbl 1230.35067) Full Text: DOI arXiv
Li, Dong; Zhang, Xiaoyi Dynamics for the energy critical nonlinear wave equation in high dimensions. (English) Zbl 1221.35248 Trans. Am. Math. Soc. 363, No. 3, 1137-1160 (2011). Reviewer: Marie Kopáčková (Praha) MSC: 35L71 35L15 35B33 35B40 35B44 PDFBibTeX XMLCite \textit{D. Li} and \textit{X. Zhang}, Trans. Am. Math. Soc. 363, No. 3, 1137--1160 (2011; Zbl 1221.35248) Full Text: DOI arXiv
Ibrahim, S.; Jrad, R. Strichartz type estimates and the well-posedness of an energy critical 2D wave equation in a bounded domain. (English) Zbl 1218.35146 J. Differ. Equations 250, No. 9, 3740-3771 (2011). Reviewer: Claudia Simionescu-Badea (Wien) MSC: 35L71 35L20 35A01 35B45 PDFBibTeX XMLCite \textit{S. Ibrahim} and \textit{R. Jrad}, J. Differ. Equations 250, No. 9, 3740--3771 (2011; Zbl 1218.35146) Full Text: DOI arXiv
Mejjaoli, H. Nonlinear generalized Dunkl-wave equations and applications. (English) Zbl 1217.35122 J. Math. Anal. Appl. 375, No. 1, 118-138 (2011). Reviewer: Valery V. Karachik (Chelyabinsk) MSC: 35L71 35L15 35L05 35B45 PDFBibTeX XMLCite \textit{H. Mejjaoli}, J. Math. Anal. Appl. 375, No. 1, 118--138 (2011; Zbl 1217.35122) Full Text: DOI
Mejjaoli, H. Nonlinear Dunkl-wave equations. (English) Zbl 1204.35121 Appl. Anal. 89, No. 10, 1645-1668 (2010). MSC: 35L71 35L15 35B45 PDFBibTeX XMLCite \textit{H. Mejjaoli}, Appl. Anal. 89, No. 10, 1645--1668 (2010; Zbl 1204.35121) Full Text: DOI
Ibrahim, Slim; Majdoub, Mohamed; Masmoudi, Nader; Nakanishi, Kenji Scattering for the two-dimensional energy-critical wave equation. (English) Zbl 1206.35175 Duke Math. J. 150, No. 2, 287-329 (2009). Reviewer: Dimitar A. Kolev (Sofia) MSC: 35L71 81Q05 35Q55 35B40 35B33 37K05 37L50 PDFBibTeX XMLCite \textit{S. Ibrahim} et al., Duke Math. J. 150, No. 2, 287--329 (2009; Zbl 1206.35175) Full Text: DOI arXiv
Kenig, Carlos E.; Merle, Frank Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. (English) Zbl 1183.35202 Acta Math. 201, No. 2, 147-212 (2008). Reviewer: Marie Kopáčková (Praha) MSC: 35L71 35L15 35B44 35A01 PDFBibTeX XMLCite \textit{C. E. Kenig} and \textit{F. Merle}, Acta Math. 201, No. 2, 147--212 (2008; Zbl 1183.35202) Full Text: DOI arXiv
Merle, Frank; Zaag, Hatem Openness of the set of non-characteristic points and regularity of the blow-up curve for the 1 D semilinear wave equation. (English) Zbl 1159.35046 Commun. Math. Phys. 282, No. 1, 55-86 (2008). Reviewer: Marie Kopáčková (Praha) MSC: 35L70 35B40 35L15 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, Commun. Math. Phys. 282, No. 1, 55--86 (2008; Zbl 1159.35046) Full Text: DOI
Nouaili, Nejla \(\mathcal C^{1,\alpha}\) regularity of the blow-up curve at non characteristic points for the one dimensional semilinear wave equation. (English) Zbl 1158.35335 Commun. Partial Differ. Equations 33, No. 8, 1540-1548 (2008). MSC: 35D10 35L15 35L70 PDFBibTeX XMLCite \textit{N. Nouaili}, Commun. Partial Differ. Equations 33, No. 8, 1540--1548 (2008; Zbl 1158.35335) Full Text: DOI
Kharibegashvili, S. On the solvability of the Cauchy characteristic problem for a nonlinear equation with iterated wave operator in the principal part. (English) Zbl 1138.35068 J. Math. Anal. Appl. 338, No. 1, 71-81 (2008). MSC: 35M20 35L05 35L75 PDFBibTeX XMLCite \textit{S. Kharibegashvili}, J. Math. Anal. Appl. 338, No. 1, 71--81 (2008; Zbl 1138.35068) Full Text: DOI
Kharibegashvili, S. On the solvability of one multidimensional version of the first Darboux problem for some nonlinear wave equations. (English) Zbl 1132.35418 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 4, 912-924 (2008). MSC: 35L70 35L20 PDFBibTeX XMLCite \textit{S. Kharibegashvili}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 68, No. 4, 912--924 (2008; Zbl 1132.35418) Full Text: DOI
Merle, Frank; Zaag, Hatem Existence and universality of the blow-up profile for the semilinear wave equation in one space dimension. (English) Zbl 1133.35070 J. Funct. Anal. 253, No. 1, 43-121 (2007). Reviewer: Marie Kopáčková (Praha) MSC: 35L70 35L15 35B40 PDFBibTeX XMLCite \textit{F. Merle} and \textit{H. Zaag}, J. Funct. Anal. 253, No. 1, 43--121 (2007; Zbl 1133.35070) Full Text: DOI
Kharibegashvili, S. S. On the existence or absence of global solutions for the multidimensional version of the second Darboux problem for some nonlinear hyperbolic equations. (English. Russian original) Zbl 1131.35365 Differ. Equ. 43, No. 3, 402-416 (2007); translation from Differ. Uravn. 43, No. 3, 388-401 (2007). MSC: 35L70 35L20 35A05 PDFBibTeX XMLCite \textit{S. S. Kharibegashvili}, Differ. Equ. 43, No. 3, 402--416 (2007; Zbl 1131.35365); translation from Differ. Uravn. 43, No. 3, 388--401 (2007) Full Text: DOI
Ibrahim, Slim; Majdoub, Mohamed; Masmoudi, Nader Ill-posedness of \(H^1\)-supercritical waves. (English) Zbl 1127.35073 C. R., Math., Acad. Sci. Paris 345, No. 3, 133-138 (2007). MSC: 35R25 35L70 PDFBibTeX XMLCite \textit{S. Ibrahim} et al., C. R., Math., Acad. Sci. Paris 345, No. 3, 133--138 (2007; Zbl 1127.35073) Full Text: DOI
Tao, Terence Global regularity for a logarithmically supercritical defocusing nonlinear wave equation for spherically symmetric data. (English) Zbl 1124.35043 J. Hyperbolic Differ. Equ. 4, No. 2, 259-265 (2007). Reviewer: Petar Popivanov (Sofia) MSC: 35L70 35L15 PDFBibTeX XMLCite \textit{T. Tao}, J. Hyperbolic Differ. Equ. 4, No. 2, 259--265 (2007; Zbl 1124.35043) Full Text: DOI arXiv
Kharibegashvili, S. S. On the nonexistence of global solutions of the characteristic Cauchy problem for a nonlinear wave equation in a conical domain. (English. Russian original) Zbl 1131.35366 Differ. Equ. 42, No. 2, 279-290 (2006); translation from Differ. Uravn. 42, No. 2, 261-271 (2006). MSC: 35L70 35L15 PDFBibTeX XMLCite \textit{S. S. Kharibegashvili}, Differ. Equ. 42, No. 2, 279--290 (2006; Zbl 1131.35366); translation from Differ. Uravn. 42, No. 2, 261--271 (2006) Full Text: DOI
Zelik, S. V. The attractor of a quasilinear hyperbolic equation with dissipation in \(\mathbb{R}^n\): Dimension and \(\varepsilon\)-entropy. (English. Russian original) Zbl 0974.35016 Math. Notes 67, No. 2, 248-251 (2000); translation from Mat. Zametki 67, No. 2, 304-308 (2000). Reviewer: Victor Sharapov (Volgograd) MSC: 35B41 35L70 37L30 35L15 PDFBibTeX XMLCite \textit{S. V. Zelik}, Math. Notes 67, No. 2, 248--251 (2000; Zbl 0974.35016); translation from Mat. Zametki 67, No. 2, 304--308 (2000) Full Text: DOI
Nakamura, M.; Ozawa, T. The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space. (English) Zbl 0960.35066 Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 2, 199-215 (1999). Reviewer: H.Tanabe (Toyonaka) MSC: 35L70 35L15 35L05 PDFBibTeX XMLCite \textit{M. Nakamura} and \textit{T. Ozawa}, Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 2, 199--215 (1999; Zbl 0960.35066) Full Text: Numdam EuDML
Belchev, Eugene; Kepka, Mariusz; Zhou, Zhengfang Global existence of solutions to nonlinear wave equations. (English) Zbl 0938.35107 Commun. Partial Differ. Equations 24, No. 11-12, 2297-2331 (1999). Reviewer: R.Precup (Cluj-Napoca) MSC: 35L70 35A22 35L15 PDFBibTeX XMLCite \textit{E. Belchev} et al., Commun. Partial Differ. Equations 24, No. 11--12, 2297--2331 (1999; Zbl 0938.35107) Full Text: DOI
Struwe, Michael Uniqueness for critical nonlinear wave equations and wave maps via the energy inequality. (English) Zbl 0933.35141 Commun. Pure Appl. Math. 52, No. 9, 1179-1188 (1999). Reviewer: Michael Struwe MSC: 35L70 35L15 PDFBibTeX XMLCite \textit{M. Struwe}, Commun. Pure Appl. Math. 52, No. 9, 1179--1188 (1999; Zbl 0933.35141) Full Text: DOI
Nakanishi, Kenji Unique global existence and asymptotic behaviour of solutions for wave equations with non-coercive critical nonlinearity. (English) Zbl 0926.35022 Commun. Partial Differ. Equations 24, No. 1-2, 185-221 (1999). Reviewer: Vadim Komkov (Florida) MSC: 35B40 35L70 35L15 PDFBibTeX XMLCite \textit{K. Nakanishi}, Commun. Partial Differ. Equations 24, No. 1--2, 185--221 (1999; Zbl 0926.35022) Full Text: DOI
Bahouri, Hajer; Shatah, Jalal Decay estimates for the critical semilinear wave equation. (English) Zbl 0924.35084 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 6, 783-789 (1998). Reviewer: Marie Kopáčková (Praha) MSC: 35L70 35B40 PDFBibTeX XMLCite \textit{H. Bahouri} and \textit{J. Shatah}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 15, No. 6, 783--789 (1998; Zbl 0924.35084) Full Text: DOI Numdam EuDML
Feireisl, Eduard Asymptotic behaviour and attractors for a semilinear damped wave equation with supercritical exponent. (English) Zbl 0838.35078 Proc. R. Soc. Edinb., Sect. A 125, No. 5, 1051-1062 (1995). Reviewer: R.Precup (Cluj-Napoca) MSC: 35L70 35L15 35B40 PDFBibTeX XMLCite \textit{E. Feireisl}, Proc. R. Soc. Edinb., Sect. A, Math. 125, No. 5, 1051--1062 (1995; Zbl 0838.35078) Full Text: DOI
Kapitanski, Lev Weak and yet weaker solutions of semilinear wave equations. (English) Zbl 0831.35109 Commun. Partial Differ. Equations 19, No. 9-10, 1629-1676 (1994). Reviewer: S.A.Spagnolo (Pisa) MSC: 35L70 35L15 35D05 PDFBibTeX XMLCite \textit{L. Kapitanski}, Commun. Partial Differ. Equations 19, No. 9--10, 1629--1676 (1994; Zbl 0831.35109) Full Text: DOI
Ginibre, J.; Velo, G. Regularity of solutions of critical and subcritical nonlinear wave equations. (English) Zbl 0831.35108 Nonlinear Anal., Theory Methods Appl. 22, No. 1, 1-19 (1994). Reviewer: J.Ginibre (Orsay) MSC: 35L70 35B65 35L15 PDFBibTeX XMLCite \textit{J. Ginibre} and \textit{G. Velo}, Nonlinear Anal., Theory Methods Appl. 22, No. 1, 1--19 (1994; Zbl 0831.35108) Full Text: DOI
Feireisl, Eduard On the dynamics of semilinear damped wave equations on \(\mathbb{R}^ N\). (English) Zbl 0823.35118 Commun. Partial Differ. Equations 18, No. 12, 1981-1999 (1993). Reviewer: R.Racke (Konstanz) MSC: 35L70 35B40 PDFBibTeX XMLCite \textit{E. Feireisl}, Commun. Partial Differ. Equations 18, No. 12, 1981--1999 (1993; Zbl 0823.35118) Full Text: DOI