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## Biler, Piotr

Compute Distance To:
 Author ID: biler.piotr Published as: Biler, B.; Biler, P.; Biler, Piotr Homepage: http://www.math.uni.wroc.pl/~biler/ External Links: MGP · Wikidata · ResearchGate
 Documents Indexed: 106 Publications since 1984, including 5 Books Reviewing Activity: 432 Reviews
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#### Co-Authors

 39 single-authored 27 Karch, Grzegorz 21 Nadzieja, Tadeusz 9 Woyczynski, Wojbor A. 6 Dolbeault, Jean 6 Zienkiewicz, Jacek 5 Laurençot, Philippe 4 Guerra, Ignacio A. 3 Esteban, Maria J. 3 Stańczy, Robert 2 Brandolese, Lorenzo 2 Cannone, Marco 2 Funaki, Tadahisa 2 Hebisch, Waldemar 2 Imbert, Cyril 2 Krzywicki, Andrzej 2 Markowich, Peter Alexander 2 Pilarczyk, Dominika 2 Witkowski, Alfred 1 Boritchev, Alexandre 1 Cieślak, Tomasz 1 Corrias, Lucilla 1 Dziubański, Jacek 1 Espejo, Elio E. 1 Guedda, Mohammed 1 Hilhorst, Danielle 1 Monneau, Régis 1 Raczyński, Andrzej 1 Tabisz, Krzysztof 1 Wu, Gang
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#### Serials

 8 Colloquium Mathematicum 5 Mathematical Methods in the Applied Sciences 5 Nonlinear Analysis. Theory, Methods & Applications 4 Studia Mathematica 3 Journal of Differential Equations 3 Bulletin of the Polish Academy of Sciences, Mathematics 3 Topological Methods in Nonlinear Analysis 3 Advances in Differential Equations 3 Journal of Evolution Equations 2 Applicable Analysis 2 Nonlinearity 2 Reports on Mathematical Physics 2 Commentationes Mathematicae Universitatis Carolinae 2 Monatshefte für Mathematik 2 Roczniki Polskiego Towarzystwa Matematycznego. Seria II. Wiadomości Matematyczne 2 Advances in Mathematical Sciences and Applications 2 Applicationes Mathematicae 2 Communications on Pure and Applied Analysis 2 Banach Center Publications 2 Pure and Applied Mathematics, Marcel Dekker 1 American Mathematical Monthly 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Journal of Mathematical Biology 1 Letters in Mathematical Physics 1 Transport Theory and Statistical Physics 1 Advances in Mathematics 1 Annales Polonici Mathematici 1 Demonstratio Mathematica 1 Mathematische Annalen 1 Mathematicae Notae 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Probability and Mathematical Statistics 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Annales Scientifiques de l’Université de Clermont-Ferrand II. Probabilités et Applications 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Applied Mathematics Letters 1 Differential and Integral Equations 1 Communications in Partial Differential Equations 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 SIAM Journal on Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 NoDEA. Nonlinear Differential Equations and Applications 1 Discrete and Continuous Dynamical Systems 1 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 1 Annales Henri Poincaré 1 Annales Mathematicae Silesianae 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Folia Mathematica 1 Networks and Heterogeneous Media 1 De Gruyter Series in Mathematics and Life Sciences
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#### Fields

 101 Partial differential equations (35-XX) 29 Statistical mechanics, structure of matter (82-XX) 18 Biology and other natural sciences (92-XX) 8 Fluid mechanics (76-XX) 4 Ordinary differential equations (34-XX) 4 Probability theory and stochastic processes (60-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Integral equations (45-XX) 2 History and biography (01-XX) 2 Sequences, series, summability (40-XX) 2 Operator theory (47-XX) 2 Quantum theory (81-XX) 2 Astronomy and astrophysics (85-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of deformable solids (74-XX)

#### Citations contained in zbMATH

84 Publications have been cited 1,550 times in 861 Documents Cited by Year
Local and global solvability of some parabolic systems modelling chemotaxis. Zbl 0913.35021
Biler, Piotr
1998
The Debye system: Existence and large time behavior of solutions. Zbl 0814.35054
1994
Fractal Burgers equations. Zbl 0911.35100
Biler, Piotr; Funaki, Tadahisa; Woyczynski, Wojbor A.
1998
Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems. Zbl 0976.82046
Biler, Piotr; Dolbeault, Jean
2000
Global solutions to some parabolic-elliptic systems of chemotaxis. Zbl 0941.35009
Biler, Piotr
1999
Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws. Zbl 0991.35009
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A.
2001
Existence and nonexistence of solutions for a model of gravitational interaction of particles. I. Zbl 0817.35041
1994
The $$8\pi$$-problem for radially symmetric solutions of a chemotaxis model in the plane. Zbl 1105.35131
2006
Blowup of solutions to generalized Keller-Segel model. Zbl 1239.35177
Biler, Piotr; Karch, Grzegorz
2010
Nonlinear diffusion of dislocation density and self-similar solutions. Zbl 1207.82049
Biler, Piotr; Karch, Grzegorz; Monneau, Régis
2010
Global and exploding solutions for nonlocal quadratic evolution problems. Zbl 0940.35035
Biler, Piotr; Woyczynski, Wojbor A.
1999
Existence and nonexistence of solutions for a model of gravitational interaction of particles. III. Zbl 0836.35076
Biler, Piotr
1995
Attractors for the system of Schrödinger and Klein-Gordon equations with Yukawa coupling. Zbl 0725.35020
Biler, Piotr
1990
The nonlocal porous medium equation: Barenblatt profiles and other weak solutions. Zbl 1308.35197
Biler, Piotr; Imbert, Cyril; Karch, Grzegorz
2015
Existence and nonexistence of solutions for a model of gravitational interaction of particles. II. Zbl 0832.35015
1994
Remark on the decay for damped string and beam equations. Zbl 0611.35057
Biler, Piotr
1986
Two-dimensional chemotaxis models with fractional diffusion. Zbl 1163.35490
Biler, Piotr; Wu, Gang
2009
Blowup in higher dimensional two species chemotactic systems. Zbl 1278.35250
Biler, Piotr; Espejo, Elio E.; Guerra, Ignacio
2013
Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis. Zbl 1230.92011
Biler, Piotr; Corrias, Lucilla; Dolbeault, Jean
2011
Barenblatt profiles for a nonlocal porous medium equation. Zbl 1221.35209
Biler, Piotr; Imbert, Cyril; Karch, Grzegorz
2011
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation. Zbl 0829.35044
Biler, Piotr
1995
Asymptotics for conservation laws involving Lévy diffusion generators. Zbl 0990.35023
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A.
2001
Global regular and singular solutions for a model of gravitating particles. Zbl 1078.35097
Biler, Piotr; Cannone, Marco; Guerra, Ignacio A.; Karch, Grzegorz
2004
Asymptotics for multifractal conservation laws. Zbl 0931.35015
Biler, Piotr; Karch, Grzegorz; Woyczynski, Wojbor A.
1999
Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions. Zbl 0781.35025
Biler, Piotr
1992
Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation. Zbl 1056.35024
Biler, Piotr; Guedda, Mohammed; Karch, Grzegorz
2004
Long time behavior of solutions of the generalized Benjamin-Bona-Mahony equation in two space dimensions. Zbl 0759.35012
Biler, Piotr
1992
Asymptotic behaviour in time of solutions to some equations generalizing the Korteweg-de Vries-Burgers equation. Zbl 0561.35064
Biler, Piotr
1984
Local criteria for blowup in two-dimensional chemotaxis models. Zbl 1360.35290
Biler, Piotr; Cieślak, Tomasz; Karch, Grzegorz; Zienkiewicz, Jacek
2017
Large-time behaviour of periodic solutions to dissipative equations of Korteweg-de Vries-Burgers type. Zbl 0561.35065
Biler, Piotr
1984
Optimal criteria for blowup of radial and $$N$$-symmetric solutions of chemotaxis systems. Zbl 1329.35316
Biler, Piotr; Karch, Grzegorz; Zienkiewicz, Jacek
2015
Multifractal and Lévy conservation laws. Zbl 0945.35015
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A.
2000
Interacting particle approximation for nonlocal quadratic evolution problems. Zbl 0985.60091
Biler, Piotr; Funaki, Tadahisa; Woyczynski, Wojbor A.
1999
The $$8\pi$$-problem for radially symmetric solutions of a chemotaxis model in a disc. Zbl 1135.35367
2006
Nonisothermal systems of self-attracting Fermi-Dirac particles. Zbl 1146.35415
2004
Growth and accretion of mass in an astrophysical model. Zbl 0838.35105
Biler, P.
1995
Blowup and self-similar solutions for two-component drift-diffusion systems. Zbl 1251.35171
Biler, Piotr; Guerra, Ignacio
2012
On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis. Zbl 1167.35316
Biler, Piotr; Brandolese, Lorenzo
2009
A nonlocal singular parabolic problem modelling gravitational interaction of particles. Zbl 0952.35008
1998
A class of nonlocal parabolic problems occurring in statistical mechanics. Zbl 0818.35046
1993
Global and exploding solutions in a model of self-gravitating systems. Zbl 1043.85001
2003
Blowup of solutions to a diffusive aggregation model. Zbl 1177.35188
Biler, Piotr; Karch, Grzegorz; Laurençot, Philippe
2009
Radially symmetric solutions of a chemotaxis model in the plane – the supercritical case. Zbl 1153.35395
Biler, Piotr
2008
Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane. Zbl 1326.35398
Biler, Piotr; Guerra, Ignacio; Karch, Grzegorz
2015
Large time asymptotics of nonlinear drift-diffusion systems with Poisson coupling. Zbl 0988.35134
Biler, Piotr; Dolbeault, Jean; Markowich, Peter A.
2001
Large global-in-time solutions to a nonlocal model of chemotaxis. Zbl 1398.35248
Biler, Piotr; Karch, Grzegorz; Zienkiewicz, Jacek
2018
Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data. Zbl 1326.35399
Biler, Piotr; Zienkiewicz, Jacek
2015
Problems in mathematical analysis. Zbl 0697.00003
Biler, Piotr; Witkowski, Alfred
1990
Steady states for Streater’s energy-transport models of self-gravitating particles. Zbl 1044.82013
Biler, Piotr; Dolbeault, Jean; Esteban, Maria J.; Markowich, Peter A.; Nadzieja, Tadeusz
2004
Time decay of solutions of semilinear strongly damped generalized wave equations. Zbl 0753.35011
Biler, Piotr
1991
Morrey spaces norms and criteria for blowup in chemotaxis models. Zbl 1333.35299
Biler, Piotr; Karch, Grzegorz; Zienkiewicz, Jacek
2016
On an evolution system describing self-gravitating Fermi-Dirac particles. Zbl 1103.35086
2004
Generalized Fokker–Planck equations and convergence to their equilibria. Zbl 1024.35013
Biler, Piotr; Karch, Grzegorz
2003
Self-interaction of Brownian particles coupled with thermodynamic processes. Zbl 1010.82028
1998
A singular problem in electrolytes theory. Zbl 0885.35051
1997
Scattering of small solutions to generalized Benjamin-Bona-Mahony equation in several space dimensions. Zbl 0796.35142
Biler, Piotr; Dziubański, Jacek; Hebisch, Waldemar
1992
Nonlinear diffusion models for self-gravitating particles. Zbl 1113.35328
Biler, Piotr; Stańczy, Robert
2007
A note on the paper of Y. Naito: “Asymptotically self-similar solutions for the parabolic system modelling chemotaxis”. Zbl 1116.35054
Biler, Piotr
2006
Local and global solutions of a nonlinear nonlocal parabolic problem. Zbl 0877.35054
Biler, Piotr
1995
Growth and accretion of mass in an astrophysical model. II. Zbl 0845.35011
1995
A singular perturbation problem for nonlinear damped hyperbolic equations. Zbl 0701.35013
Biler, Piotr
1989
Regular decay of solutions of strongly damped nonlinear hyperbolic equations. Zbl 0666.34072
Biler, Piotr
1989
Exponential decay of solutions of damped nonlinear hyperbolic equations. Zbl 0656.35091
Biler, Piotr
1987
Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis. Zbl 1417.35208
Biler, Piotr; Zienkiewicz, Jacek
2019
Intermediate asymptotics in $$L^{1}$$ for general nonlinear diffusion equations. Zbl 1011.35019
Biler, P.; Dolbeault, J.; Esteban, M. J.
2002
Structure of steady states for Streater’s energy-transport models of gravitating particles. Zbl 1008.35052
2002
Nonlocal quadratic evolution problems. Zbl 0953.35070
Biler, Piotr; Woyczyński, Wojbor A.
2000
Nonlocal parabolic problems in statistical mechanics. Zbl 0892.35073
1997
Asymptotic stability of Navier-Stokes flow past an obstacle. Zbl 1161.35459
Biler, Piotr; Cannone, Marco; Karch, Grzegorz
2004
A Neumann problem for a convection-diffusion equation on the half-line. Zbl 1003.35065
Biler, Piotr; Karch, Grzegorz
2000
Problems and examples in differential equations. Zbl 0760.34001
1992
Stochastic interpretation of potential scattering in quantum mechanics. Zbl 0534.60052
Biler, P.
1984
Around a singular solution of a nonlocal nonlinear heat equation. Zbl 1407.35105
Biler, Piotr; Pilarczyk, Dominika
2019
Blowup versus global in time existence of solutions for nonlinear heat equations. Zbl 1408.35072
Biler, Piotr
2018
Mathematical challenges in the theory of chemotaxis. Zbl 1403.35300
Biler, Piotr
2018
Mean field models for self-gravitating particles. Zbl 1181.35290
Biler, Piotr; Stańczy, Robert
2006
Global existence versus blow up for some models of interacting particles. Zbl 1116.35015
Biler, Piotr; Brandolese, Lorenzo
2006
Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Zbl 1104.35004
Biler, Piotr (ed.); Karch, Grzegorz (ed.)
2006
Entropy methods and intermediate asymptotics for nonlinear drift-diffusion systems. Zbl 1091.35504
Biler, Piotr
2002
Steady states and long time asymptotics of solutions of Streater’s models. Zbl 1046.82020
Biler, Piotr
2001
Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater’s models. Zbl 1003.35120
Biler, Piotr; Karch, Grzegorz; Dolbeault, Jean; Esteban, Maria J.
2001
Asymptotics and high dimensional approximations for nonlinear pseudodifferential equations involving Lévy generators. Zbl 0986.35148
Biler, P.; Karch, G.; Woyczyński, W. A.
2001
On the stationary solutions of Burgers’ equation. Zbl 0635.35008
Biler, Piotr
1987
Asymptotic behaviour in time of solutions to some equations generalizing the Korteweg-de Vries-Burgers equation. Zbl 0581.35071
Biler, Piotr
1985
Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis. Zbl 1417.35208
Biler, Piotr; Zienkiewicz, Jacek
2019
Around a singular solution of a nonlocal nonlinear heat equation. Zbl 1407.35105
Biler, Piotr; Pilarczyk, Dominika
2019
Large global-in-time solutions to a nonlocal model of chemotaxis. Zbl 1398.35248
Biler, Piotr; Karch, Grzegorz; Zienkiewicz, Jacek
2018
Blowup versus global in time existence of solutions for nonlinear heat equations. Zbl 1408.35072
Biler, Piotr
2018
Mathematical challenges in the theory of chemotaxis. Zbl 1403.35300
Biler, Piotr
2018
Local criteria for blowup in two-dimensional chemotaxis models. Zbl 1360.35290
Biler, Piotr; Cieślak, Tomasz; Karch, Grzegorz; Zienkiewicz, Jacek
2017
Morrey spaces norms and criteria for blowup in chemotaxis models. Zbl 1333.35299
Biler, Piotr; Karch, Grzegorz; Zienkiewicz, Jacek
2016
The nonlocal porous medium equation: Barenblatt profiles and other weak solutions. Zbl 1308.35197
Biler, Piotr; Imbert, Cyril; Karch, Grzegorz
2015
Optimal criteria for blowup of radial and $$N$$-symmetric solutions of chemotaxis systems. Zbl 1329.35316
Biler, Piotr; Karch, Grzegorz; Zienkiewicz, Jacek
2015
Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane. Zbl 1326.35398
Biler, Piotr; Guerra, Ignacio; Karch, Grzegorz
2015
Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data. Zbl 1326.35399
Biler, Piotr; Zienkiewicz, Jacek
2015
Blowup in higher dimensional two species chemotactic systems. Zbl 1278.35250
Biler, Piotr; Espejo, Elio E.; Guerra, Ignacio
2013
Blowup and self-similar solutions for two-component drift-diffusion systems. Zbl 1251.35171
Biler, Piotr; Guerra, Ignacio
2012
Large mass self-similar solutions of the parabolic-parabolic Keller-Segel model of chemotaxis. Zbl 1230.92011
Biler, Piotr; Corrias, Lucilla; Dolbeault, Jean
2011
Barenblatt profiles for a nonlocal porous medium equation. Zbl 1221.35209
Biler, Piotr; Imbert, Cyril; Karch, Grzegorz
2011
Blowup of solutions to generalized Keller-Segel model. Zbl 1239.35177
Biler, Piotr; Karch, Grzegorz
2010
Nonlinear diffusion of dislocation density and self-similar solutions. Zbl 1207.82049
Biler, Piotr; Karch, Grzegorz; Monneau, Régis
2010
Two-dimensional chemotaxis models with fractional diffusion. Zbl 1163.35490
Biler, Piotr; Wu, Gang
2009
On the parabolic-elliptic limit of the doubly parabolic Keller–Segel system modelling chemotaxis. Zbl 1167.35316
Biler, Piotr; Brandolese, Lorenzo
2009
Blowup of solutions to a diffusive aggregation model. Zbl 1177.35188
Biler, Piotr; Karch, Grzegorz; Laurençot, Philippe
2009
Radially symmetric solutions of a chemotaxis model in the plane – the supercritical case. Zbl 1153.35395
Biler, Piotr
2008
Nonlinear diffusion models for self-gravitating particles. Zbl 1113.35328
Biler, Piotr; Stańczy, Robert
2007
The $$8\pi$$-problem for radially symmetric solutions of a chemotaxis model in the plane. Zbl 1105.35131
2006
The $$8\pi$$-problem for radially symmetric solutions of a chemotaxis model in a disc. Zbl 1135.35367
2006
A note on the paper of Y. Naito: “Asymptotically self-similar solutions for the parabolic system modelling chemotaxis”. Zbl 1116.35054
Biler, Piotr
2006
Mean field models for self-gravitating particles. Zbl 1181.35290
Biler, Piotr; Stańczy, Robert
2006
Global existence versus blow up for some models of interacting particles. Zbl 1116.35015
Biler, Piotr; Brandolese, Lorenzo
2006
Self-similar solutions of nonlinear PDE. Selected papers of the conference, Bȩdlewo, Poland, September 5–9, 2005. Zbl 1104.35004
Biler, Piotr (ed.); Karch, Grzegorz (ed.)
2006
Global regular and singular solutions for a model of gravitating particles. Zbl 1078.35097
Biler, Piotr; Cannone, Marco; Guerra, Ignacio A.; Karch, Grzegorz
2004
Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation. Zbl 1056.35024
Biler, Piotr; Guedda, Mohammed; Karch, Grzegorz
2004
Nonisothermal systems of self-attracting Fermi-Dirac particles. Zbl 1146.35415
2004
Steady states for Streater’s energy-transport models of self-gravitating particles. Zbl 1044.82013
Biler, Piotr; Dolbeault, Jean; Esteban, Maria J.; Markowich, Peter A.; Nadzieja, Tadeusz
2004
On an evolution system describing self-gravitating Fermi-Dirac particles. Zbl 1103.35086
2004
Asymptotic stability of Navier-Stokes flow past an obstacle. Zbl 1161.35459
Biler, Piotr; Cannone, Marco; Karch, Grzegorz
2004
Global and exploding solutions in a model of self-gravitating systems. Zbl 1043.85001
2003
Generalized Fokker–Planck equations and convergence to their equilibria. Zbl 1024.35013
Biler, Piotr; Karch, Grzegorz
2003
Intermediate asymptotics in $$L^{1}$$ for general nonlinear diffusion equations. Zbl 1011.35019
Biler, P.; Dolbeault, J.; Esteban, M. J.
2002
Structure of steady states for Streater’s energy-transport models of gravitating particles. Zbl 1008.35052
2002
Entropy methods and intermediate asymptotics for nonlinear drift-diffusion systems. Zbl 1091.35504
Biler, Piotr
2002
Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws. Zbl 0991.35009
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A.
2001
Asymptotics for conservation laws involving Lévy diffusion generators. Zbl 0990.35023
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A.
2001
Large time asymptotics of nonlinear drift-diffusion systems with Poisson coupling. Zbl 0988.35134
Biler, Piotr; Dolbeault, Jean; Markowich, Peter A.
2001
Steady states and long time asymptotics of solutions of Streater’s models. Zbl 1046.82020
Biler, Piotr
2001
Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater’s models. Zbl 1003.35120
Biler, Piotr; Karch, Grzegorz; Dolbeault, Jean; Esteban, Maria J.
2001
Asymptotics and high dimensional approximations for nonlinear pseudodifferential equations involving Lévy generators. Zbl 0986.35148
Biler, P.; Karch, G.; Woyczyński, W. A.
2001
Long time behavior of solutions of Nernst-Planck and Debye-Hückel drift-diffusion systems. Zbl 0976.82046
Biler, Piotr; Dolbeault, Jean
2000
Multifractal and Lévy conservation laws. Zbl 0945.35015
Biler, Piotr; Karch, Grzegorz; Woyczyński, Wojbor A.
2000
Nonlocal quadratic evolution problems. Zbl 0953.35070
Biler, Piotr; Woyczyński, Wojbor A.
2000
A Neumann problem for a convection-diffusion equation on the half-line. Zbl 1003.35065
Biler, Piotr; Karch, Grzegorz
2000
Global solutions to some parabolic-elliptic systems of chemotaxis. Zbl 0941.35009
Biler, Piotr
1999
Global and exploding solutions for nonlocal quadratic evolution problems. Zbl 0940.35035
Biler, Piotr; Woyczynski, Wojbor A.
1999
Asymptotics for multifractal conservation laws. Zbl 0931.35015
Biler, Piotr; Karch, Grzegorz; Woyczynski, Wojbor A.
1999
Interacting particle approximation for nonlocal quadratic evolution problems. Zbl 0985.60091
Biler, Piotr; Funaki, Tadahisa; Woyczynski, Wojbor A.
1999
Local and global solvability of some parabolic systems modelling chemotaxis. Zbl 0913.35021
Biler, Piotr
1998
Fractal Burgers equations. Zbl 0911.35100
Biler, Piotr; Funaki, Tadahisa; Woyczynski, Wojbor A.
1998
A nonlocal singular parabolic problem modelling gravitational interaction of particles. Zbl 0952.35008
1998
Self-interaction of Brownian particles coupled with thermodynamic processes. Zbl 1010.82028
1998
A singular problem in electrolytes theory. Zbl 0885.35051
1997
Nonlocal parabolic problems in statistical mechanics. Zbl 0892.35073
1997
Existence and nonexistence of solutions for a model of gravitational interaction of particles. III. Zbl 0836.35076
Biler, Piotr
1995
The Cauchy problem and self-similar solutions for a nonlinear parabolic equation. Zbl 0829.35044
Biler, Piotr
1995
Growth and accretion of mass in an astrophysical model. Zbl 0838.35105
Biler, P.
1995
Local and global solutions of a nonlinear nonlocal parabolic problem. Zbl 0877.35054
Biler, Piotr
1995
Growth and accretion of mass in an astrophysical model. II. Zbl 0845.35011
1995
The Debye system: Existence and large time behavior of solutions. Zbl 0814.35054
1994
Existence and nonexistence of solutions for a model of gravitational interaction of particles. I. Zbl 0817.35041
1994
Existence and nonexistence of solutions for a model of gravitational interaction of particles. II. Zbl 0832.35015
1994
A class of nonlocal parabolic problems occurring in statistical mechanics. Zbl 0818.35046
1993
Existence and asymptotics of solutions for a parabolic-elliptic system with nonlinear no-flux boundary conditions. Zbl 0781.35025
Biler, Piotr
1992
Long time behavior of solutions of the generalized Benjamin-Bona-Mahony equation in two space dimensions. Zbl 0759.35012
Biler, Piotr
1992
Scattering of small solutions to generalized Benjamin-Bona-Mahony equation in several space dimensions. Zbl 0796.35142
Biler, Piotr; Dziubański, Jacek; Hebisch, Waldemar
1992
Problems and examples in differential equations. Zbl 0760.34001
1992
Time decay of solutions of semilinear strongly damped generalized wave equations. Zbl 0753.35011
Biler, Piotr
1991
Attractors for the system of Schrödinger and Klein-Gordon equations with Yukawa coupling. Zbl 0725.35020
Biler, Piotr
1990
Problems in mathematical analysis. Zbl 0697.00003
Biler, Piotr; Witkowski, Alfred
1990
A singular perturbation problem for nonlinear damped hyperbolic equations. Zbl 0701.35013
Biler, Piotr
1989
Regular decay of solutions of strongly damped nonlinear hyperbolic equations. Zbl 0666.34072
Biler, Piotr
1989
Exponential decay of solutions of damped nonlinear hyperbolic equations. Zbl 0656.35091
Biler, Piotr
1987
On the stationary solutions of Burgers’ equation. Zbl 0635.35008
Biler, Piotr
1987
Remark on the decay for damped string and beam equations. Zbl 0611.35057
Biler, Piotr
1986
Asymptotic behaviour in time of solutions to some equations generalizing the Korteweg-de Vries-Burgers equation. Zbl 0581.35071
Biler, Piotr
1985
Asymptotic behaviour in time of solutions to some equations generalizing the Korteweg-de Vries-Burgers equation. Zbl 0561.35064
Biler, Piotr
1984
Large-time behaviour of periodic solutions to dissipative equations of Korteweg-de Vries-Burgers type. Zbl 0561.35065
Biler, Piotr
1984
Stochastic interpretation of potential scattering in quantum mechanics. Zbl 0534.60052
Biler, P.
1984
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#### Cited by 968 Authors

 38 Winkler, Michael 35 Biler, Piotr 25 Karch, Grzegorz 21 Vazquez, Juan Luis 17 Laurençot, Philippe 14 Carrillo de la Plata, José Antonio 13 Mu, Chunlai 13 Zhao, Jihong 12 Ogawa, Takayoshi 11 Dolbeault, Jean 11 Naumkin, Pavel Ivanovich 10 Lankeit, Johannes 10 Mizoguchi, Noriko 10 Nagai, Toshitaka 9 Granero Belinchón, Rafael 9 Kaikina, Elena Igorevna 9 Senba, Takasi 9 Sugiyama, Yoshie 9 Suzuki, Takashi 9 Tao, Youshan 9 Woyczynski, Wojbor A. 8 Calvez, Vincent 8 Cieślak, Tomasz 8 Ferreira, Lucas Catão de Freitas 8 Fujie, Kentarou 8 Liu, Chun 8 Wang, Weike 7 Cui, Shangbin 7 Imbert, Cyril 7 Lin, Ke 7 Nadzieja, Tadeusz 7 Stinner, Christian 7 Yamamoto, Masakazu 6 Black, Tobias 6 Blanchet, Adrien 6 Burczak, Jan 6 Das, Kinkar Chandra 6 Deng, Chao 6 Hayashi, Nakao 6 Jakobsen, Espen Robstad 6 Liu, Zuhan 6 Negreanu, Mihaela 6 Perthame, Benoît 6 Shi, Qihong 6 Souplet, Philippe 6 Stańczy, Robert 6 Tello, José Ignacio 6 Wang, Shu 6 Wang, Wei 6 Zheng, Sining 6 Zienkiewicz, Jacek 5 Alibaud, Nathaël 5 Bona, Jerry Lloyd 5 del Teso, Félix 5 Duan, Jinqiao 5 Fan, Jishan 5 Guo, Boling 5 Hsieh, Chia-Yu 5 Iagar, Razvan Gabriel 5 Kurokiba, Masaki 5 Li, Yuxiang 5 Shishmarev, Ilya Andreevich 5 Wakui, Hiroshi 5 Wang, Bixiang 5 Wang, Yifu 5 Wu, Jianglun 5 Yamada, Tetsuya 5 Zhang, Linghai 5 Zhang, Qian 5 Zhang, Qingshan 5 Zhou, Ling 4 Bedrossian, Jacob 4 Bertozzi, Andrea Louise 4 Caffarelli, Luis Ángel 4 Cifani, Simone 4 Corrias, Lucilla 4 Gagneux, Gérard 4 Iwabuchi, Tsukasa 4 Korpusov, Maksim Olegovich 4 Laurent, Thomas 4 Li, Dong 4 Li, Xie 4 Lin, Taichia 4 Liu, Ji 4 Lv, Guangying 4 Millet, Olivier 4 Osaki, Koichi 4 Park, Jong Yeoul 4 Stan, Diana 4 Tarasov, Vasily E. 4 Yu, Hao 4 Zheng, Pan 4 Zheng, Xiaoxin 3 Achleitner, Franz 3 Anh, Vo V. 3 Bao, Weizhu 3 Bellomo, Nicola 3 Cannone, Marco 3 Clark, Haroldo Rodrigues 3 De Gregorio, Alessandro ...and 868 more Authors
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#### Cited in 196 Serials

 79 Journal of Differential Equations 55 Journal of Mathematical Analysis and Applications 49 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Mathematical Methods in the Applied Sciences 21 Journal of Mathematical Physics 21 Nonlinear Analysis. Real World Applications 21 Discrete and Continuous Dynamical Systems. Series B 18 Discrete and Continuous Dynamical Systems 17 Archive for Rational Mechanics and Analysis 16 SIAM Journal on Mathematical Analysis 15 Applicable Analysis 15 Journal of Functional Analysis 14 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 13 Computers & Mathematics with Applications 13 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 13 Communications in Partial Differential Equations 12 Nonlinearity 11 Applied Mathematics and Computation 11 Applied Mathematics Letters 11 Calculus of Variations and Partial Differential Equations 10 ZAMP. Zeitschrift für angewandte Mathematik und Physik 10 Journal de Mathématiques Pures et Appliquées. Neuvième Série 10 Nonlinear Analysis. Theory, Methods & Applications 9 Journal of Evolution Equations 9 Discrete and Continuous Dynamical Systems. Series S 8 Journal of Computational Physics 8 Monatshefte für Mathematik 7 Advances in Mathematics 7 Acta Applicandae Mathematicae 7 NoDEA. Nonlinear Differential Equations and Applications 7 Communications on Pure and Applied Analysis 6 Mathematische Annalen 6 Numerische Mathematik 6 Transactions of the American Mathematical Society 6 Physica D 6 Communications in Contemporary Mathematics 6 Boundary Value Problems 5 Communications in Mathematical Physics 5 Chinese Annals of Mathematics. Series B 5 Applied Numerical Mathematics 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Kinetic and Related Models 4 Communications on Pure and Applied Mathematics 4 Journal of Mathematical Biology 4 Reports on Mathematical Physics 4 Proceedings of the American Mathematical Society 4 Journal of Scientific Computing 4 Journal of Dynamics and Differential Equations 4 Fractional Calculus & Applied Analysis 4 Annales Henri Poincaré 3 Journal d’Analyse Mathématique 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Journal of Computational and Applied Mathematics 3 Mathematische Nachrichten 3 Mathematische Zeitschrift 3 Acta Mathematicae Applicatae Sinica. English Series 3 Mathematical and Computer Modelling 3 Applications of Mathematics 3 Applied Mathematical Modelling 3 SIAM Journal on Applied Mathematics 3 Stochastic Processes and their Applications 3 Bulletin des Sciences Mathématiques 3 Nonlinear Dynamics 3 Abstract and Applied Analysis 3 Journal of the European Mathematical Society (JEMS) 3 Communications in Nonlinear Science and Numerical Simulation 3 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 3 Stochastics and Dynamics 2 Journal of Statistical Physics 2 Mathematical Notes 2 Mathematics of Computation 2 BIT 2 Duke Mathematical Journal 2 Functional Analysis and its Applications 2 Manuscripta Mathematica 2 SIAM Journal on Control and Optimization 2 SIAM Journal on Numerical Analysis 2 Advances in Applied Mathematics 2 Bulletin of the Korean Mathematical Society 2 Revista Matemática Iberoamericana 2 Japan Journal of Industrial and Applied Mathematics 2 Computational Mathematics and Mathematical Physics 2 Journal of Elasticity 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2 Topological Methods in Nonlinear Analysis 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Acta Mathematica Sinica. English Series 2 Analysis and Applications (Singapore) 2 Advances in Difference Equations 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Complex Variables and Elliptic Equations 2 Networks and Heterogeneous Media 2 Mathematical Modelling of Natural Phenomena 2 Science China. Mathematics 2 Ufimskiĭ Matematicheskiĭ Zhurnal 2 Modern Stochastics. Theory and Applications 2 Séminaire Laurent Schwartz. EDP et Applications 1 International Journal of Modern Physics B ...and 96 more Serials
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#### Cited in 37 Fields

 788 Partial differential equations (35-XX) 299 Biology and other natural sciences (92-XX) 96 Fluid mechanics (76-XX) 79 Numerical analysis (65-XX) 50 Statistical mechanics, structure of matter (82-XX) 49 Probability theory and stochastic processes (60-XX) 36 Mechanics of deformable solids (74-XX) 31 Dynamical systems and ergodic theory (37-XX) 30 Operator theory (47-XX) 29 Ordinary differential equations (34-XX) 28 Real functions (26-XX) 21 Optics, electromagnetic theory (78-XX) 19 Integral equations (45-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 12 Quantum theory (81-XX) 11 Functional analysis (46-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Astronomy and astrophysics (85-XX) 7 Combinatorics (05-XX) 6 Systems theory; control (93-XX) 5 Global analysis, analysis on manifolds (58-XX) 5 Mechanics of particles and systems (70-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Functions of a complex variable (30-XX) 4 Special functions (33-XX) 4 Difference and functional equations (39-XX) 4 Classical thermodynamics, heat transfer (80-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Potential theory (31-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 1 Measure and integration (28-XX) 1 Integral transforms, operational calculus (44-XX) 1 Convex and discrete geometry (52-XX) 1 Statistics (62-XX) 1 Relativity and gravitational theory (83-XX) 1 Geophysics (86-XX)

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