Grzegorz Karch
  Instytut Matematyczny, Uniwersytet Wrocławski
 
 
Grzegorz Karch



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My publications in

Editorial work

  • Self-similar solutions of nonlinear PDE. Papers from the conference held in Będlewo, September 5–9, 2005. Edited by Piotr Biler and Grzegorz Karch. Banach Center Publications, 74. Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2006. 255 pp.
    http://dx.doi.org/10.4064/bc74

  • Nonlocal elliptic and parabolic problems. Proceedings of the conference held in Będlewo, September 12–15, 2003. Edited by Piotr Biler, Grzegorz Karch and Tadeusz Nadzieja. Banach Center Publications, 66. Polish Academy of Sciences, Institute of Mathematics, Warsaw, 2004. 351 pp.
    http://dx.doi.org/10.4064/bc66

  • Editor-in-Chief of Colloquium Matehmaticum

List of all publications

  1. Anna Marciniak-Czochra, Grzegorz Karch & Kanako Suzuki
    Instability of Turing patterns in reaction-diffusion-ODE systems
    J. Math. Biol. 74 (3) (2017), 583-618.
    http://dx.doi.org/10.1007/s00285-016-1035-z
    https://arxiv.org/abs/1301.2002

  2. Piotr Biler, Grzegorz Karch & Jacek Zienkiewicz
    Morrey spaces norms and criteria for blowup in chemotaxis models
    Netw. Heterog. Media 11 (2) (2016), 239-250.
    http://dx.doi.org/10.3934/nhm.2016.11.239

  3. Grzegorz Karch, Kanako Suzuki & Jacek Zienkiewicz
    Finite-time blowup of solutions to some activator-inhibitor systems
    Discrete Contin. Dyn. Syst. 36 (9) (2016), 4997-5010.
    http://dx.doi.org/10.3934/dcds.2016016

  4. Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki & Jacek Zienkiewicz
    Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems
    Differential Integral Equations 29 (7-8) (2016), 715-730.
    http://projecteuclid.org/euclid.die/1462298682
    https://arxiv.org/abs/1511.02510

  5. Piotr Biler, Ignacio Guerra & Grzegorz Karch
    Large global-in-time solutions of the parabolic-parabolic Keller-Segel system on the plane
    Commun. Pure Appl. Anal. 14 (6) (2015), 2117-2126.
    http://dx.doi.org/10.3934/cpaa.2015.14.2117
    https://arxiv.org/abs/1401.7650

  6. Piotr Biler, Cyril Imbert & Grzegorz Karch
    The nonlocal porous medium equation: Barenblatt profiles and other weak solutions
    Arch. Ration. Mech. Anal. 215 (2) (2015), 497-529.
    http://dx.doi.org/10.1007/s00205-014-0786-1
    https://arxiv.org/abs/1302.7219

  7. Piotr Biler, Grzegorz Karch & Jacek Zienkiewicz
    Optimal criteria for blowup of radial and N-symmetric solutions of chemotaxis systems
    Nonlinearity 28 (12) (2015), 4369-4387.
    http://dx.doi.org/10.1088/0951-7715/28/12/4369
    https://arxiv.org/abs/1407.4501

  8. Grzegorz Karch, Anna Pudełko & Xiaojing Xu
    Two-dimensional fractal Burgers equation with step-like initial conditions
    Math. Methods Appl. Sci. 38 (13) (2015), 2830-2839.
    http://dx.doi.org/10.1002/mma.3266

  9. Grzegorz Karch & Xiaoxin Zheng
    Time-dependent singularities in the Navier-Stokes system
    Discrete Contin. Dyn. Syst. 35 (7) (2015), 3039-3057.
    http://dx.doi.org/10.3934/dcds.2015.35.3039
    https://arxiv.org/abs/1401.3679

  10. Dragos Iftimie, Grzegorz Karch & Christophe Lacave
    Asymptotics of solutions to the Navier-Stokes system in exterior domains
    J. Lond. Math. Soc. (2) 90 (3) (2014), 785-806.
    http://dx.doi.org/10.1112/jlms/jdu052
    https://arxiv.org/abs/1307.7837

  11. Grzegorz Karch & Anna Marciniak-Czochra
    Instability and blow-ups in mathematical models of biological processes
    Wiad. Mat. 50 (1) (2014), 3-20.
    Article in Polish.

  12. Marco Cannone & Grzegorz Karch
    On self-similar solutions to the homogeneous Boltzmann equation
    Kinet. Relat. Models 6 (4) (2013), 801-808.
    http://dx.doi.org/10.3934/krm.2013.6.801

  13. Anna Marciniak-Czochra, Grzegorz Karch & Kanako Suzuki
    Unstable patterns in reaction-diffusion model of early carcinogenesis
    J. Math. Pures Appl. (9) 99 (5) (2013), 509-543.
    http://dx.doi.org/10.1016/j.matpur.2012.09.011
    https://arxiv.org/abs/1104.3592

  14. Piotr Biler, Cyril Imbert & Grzegorz Karch
    Barenblatt profiles for a nonlocal porous medium equation
    C. R. Math. Acad. Sci. Paris 349 (11-12) (2011), 641-645.
    http://dx.doi.org/10.1016/j.crma.2011.06.003
    https://arxiv.org/abs/1001.0910

  15. Marco Cannone, Cheng He & Grzegorz Karch
    Slowly decaying solutions to incompressible Navier-Stokes system.
    Mathematical analysis on the Navier-Stokes equations and related topics, past and future, 17-30, GAKUTO Internat. Ser. Math. Sci. Appl. 35, Gakk\=otosho, Tokyo, 2011.

  16. Dragos Iftimie, Grzegorz Karch & Christophe Lacave
    Self-similar asymptotics of solutions to the Navier-Stokes system in two dimensional exterior domain
    (2011), 1-13.
    This paper will be never published and it exists in a preprint version, only. The result from this paper is a particular case of our more general results published by us in J. Lond. Math. Soc. (2), 2014, 90, 785-806. However, ideas of proofs in both papers are different.
    http://arxiv.org/abs/1107.2054

  17. Grzegorz Karch & Dominika Pilarczyk
    Asymptotic stability of Landau solutions to Navier-Stokes system
    Arch. Ration. Mech. Anal. 202 (1) (2011), 115-131.
    http://dx.doi.org/10.1007/s00205-011-0409-z
    https://arxiv.org/abs/1104.3589

  18. Grzegorz Karch & Kanako Suzuki
    Blow-up versus global existence of solutions to aggregation equations
    Appl. Math. (Warsaw) 38 (3) (2011), 243-258.
    http://dx.doi.org/10.4064/am38-3-1
    https://arxiv.org/abs/1004.4021

  19. Nathael Alibaud, Cyril Imbert & Grzegorz Karch
    Asymptotic properties of entropy solutions to fractal Burgers equation
    SIAM J. Math. Anal. 42 (1) (2010), 354-376.
    http://dx.doi.org/10.1137/090753449
    https://arxiv.org/abs/0903.3394

  20. Piotr Biler & Grzegorz Karch
    Blowup of solutions to generalized Keller-Segel model
    J. Evol. Equ. 10 (2) (2010), 247-262.
    http://dx.doi.org/10.1007/s00028-009-0048-0

  21. Piotr Biler, Grzegorz Karch & Régis Monneau
    Nonlinear diffusion of dislocation density and self-similar solutions
    Comm. Math. Phys. 294 (1) (2010), 145-168.
    http://dx.doi.org/10.1007/s00220-009-0855-8

  22. Marco Cannone & Grzegorz Karch
    Infinite energy solutions to the homogeneous Boltzmann equation
    Comm. Pure Appl. Math. 63 (6) (2010), 747-778.
    http://dx.doi.org/10.1002/cpa.20298
    https://arxiv.org/abs/0907.1676

  23. Ahmad Fino & Grzegorz Karch
    Decay of mass for nonlinear equation with fractional Laplacian
    Monatsh. Math. 160 (4) (2010), 375-384.
    http://dx.doi.org/10.1007/s00605-009-0093-3

  24. Grzegorz Karch & Kanako Suzuki
    Spikes and diffusion waves in a one-dimensional model of chemotaxis
    Nonlinearity 23 (12) (2010), 3119-3137.
    http://dx.doi.org/10.1088/0951-7715/23/12/007
    https://arxiv.org/abs/1008.0020

  25. Piotr Biler, Grzegorz Karch & Philippe Laurençot
    Blowup of solutions to a diffusive aggregation model
    Nonlinearity 22 (7) (2009), 1559-1568.
    http://dx.doi.org/10.1088/0951-7715/22/7/003
    https://arxiv.org/abs/0903.2915

  26. Grzegorz Karch
    Nonlinear evolution equations with anomalous diffusion.
    Qualitative properties of solutions to partial differential equations, 25-68, Jind\v rich Ne\v cas Cent. Math. Model. Lect. Notes 5, Matfyzpress, Prague, 2009.

  27. Lorenzo Brandolese & Grzegorz Karch
    Far field asymptotics of solutions to convection equation with anomalous diffusion
    J. Evol. Equ. 8 (2) (2008), 307-326.
    http://dx.doi.org/10.1007/s00028-008-0356-9

  28. Grzegorz Karch, Changxing Miao & Xiaojing Xu
    On convergence of solutions of fractal Burgers equation toward rarefaction waves
    SIAM J. Math. Anal. 39 (5) (2008), 1536-1549.
    http://dx.doi.org/10.1137/070681776

  29. Grzegorz Karch & Nicolas Prioux
    Self-similarity in viscous Boussinesq equations
    Proc. Amer. Math. Soc. 136 (3) (2008), 879-888.
    http://dx.doi.org/10.1090/S0002-9939-07-09063-6

  30. Grzegorz Karch & Wojbor A. Woyczynski
    Fractal Hamilton-Jacobi-KPZ equations
    Trans. Amer. Math. Soc. 360 (5) (2008), 2423-2442.
    http://dx.doi.org/10.1090/S0002-9947-07-04389-9

  31. Piotr Biler, Grzegorz Karch, Philippe Laurençot & Tadeusz Nadzieja
    The 8pi-problem for radially symmetric solutions of a chemotaxis model in a disc
    Topol. Methods Nonlinear Anal. 27 (1) (2006), 133-147.

  32. Piotr Biler, Grzegorz Karch, Philippe Laurençot & Tadeusz Nadzieja
    The 8pi-problem for radially symmetric solutions of a chemotaxis model in the plane
    Math. Methods Appl. Sci. 29 (13) (2006), 1563-1583.
    http://dx.doi.org/10.1002/mma.743

  33. Jean Dolbeault & Grzegorz Karch
    Large time behaviour of solutions to nonhomogeneous diffusion equations.
    Self-similar solutions of nonlinear PDE, 133-147, Banach Center Publ. 74, Polish Acad. Sci. Inst. Math., Warsaw, 2006.
    http://dx.doi.org/10.4064/bc74-0-8

  34. Marco Cannone & Grzegorz Karch
    About the regularized Navier-Stokes equations
    J. Math. Fluid Mech. 7 (1) (2005), 1-28.
    http://dx.doi.org/10.1007/s00021-004-0105-y

  35. Marco Cannone & Grzegorz Karch
    On the validity of the Picard algorithm for nonlinear parabolic equations
    Proc. Roy. Soc. Edinburgh Sect. A 135 (5) (2005), 947-958.
    http://dx.doi.org/10.1017/S0308210500004212

  36. Sa\i d Benachour, Grzegorz Karch & Philippe Laurençot
    Asymptotic profiles of solutions to convection-diffusion equations
    C. R. Math. Acad. Sci. Paris 338 (5) (2004), 369-374.
    http://dx.doi.org/10.1016/j.crma.2004.01.001

  37. Sa\i d Benachour, Grzegorz Karch & Philippe Laurençot
    Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations
    J. Math. Pures Appl. (9) 83 (10) (2004), 1275-1308.
    http://dx.doi.org/10.1016/j.matpur.2004.03.002

  38. Piotr Biler, Marco Cannone, Ignacio A. Guerra & Grzegorz Karch
    Global regular and singular solutions for a model of gravitating particles
    Math. Ann. 330 (4) (2004), 693-708.
    http://dx.doi.org/10.1007/s00208-004-0565-7

  39. Piotr Biler, Marco Cannone & Grzegorz Karch
    Asymptotic stability of Navier-Stokes flow past an obstacle.
    Nonlocal elliptic and parabolic problems, 47-59, Banach Center Publ. 66, Polish Acad. Sci. Inst. Math., Warsaw, 2004.
    http://dx.doi.org/10.4064/bc66-0-4

  40. Piotr Biler, Mohammed Guedda & Grzegorz Karch
    Asymptotic properties of solutions of the viscous Hamilton-Jacobi equation
    J. Evol. Equ. 4 (1) (2004), 75-97.
    http://dx.doi.org/10.1007/s00028-003-0079-x

  41. Marco Cannone & Grzegorz Karch
    Smooth or singular solutions to the Navier-Stokes system?
    J. Differential Equations 197 (2) (2004), 247-274.
    http://dx.doi.org/10.1016/j.jde.2003.10.003

  42. Piotr Biler & Grzegorz Karch
    Generalized Fokker-Planck equations and convergence to their equilibria.
    Evolution equations (Warsaw, 2001), 307-318, Banach Center Publ. 60, Polish Acad. Sci. Inst. Math., Warsaw, 2003.

  43. Grzegorz Karch
    The heat equation.
    Workshop on Partial Differential Equations (Polish), 31-65, Lect. Notes Nonlinear Anal. 4, Juliusz Schauder Cent. Nonlinear Stud., Toru\'n, 2003.

  44. Grzegorz Karch
    Sixth millennium problem: existence and regularity of solutions of the Navier-Stokes system
    Wiadom. Mat. 38 (2002), 121-130.
    Article in Polish.

  45. Grzegorz Karch & Maria Elena Schonbek
    On zero mass solutions of viscous conservation laws
    Comm. Partial Differential Equations 27 (9-10) (2002), 2071-2100.
    http://dx.doi.org/10.1081/PDE-120016137

  46. Piotr Biler, Grzegorz Karch, Jean Dolbeault & Maria J. Esteban
    Stationary solutions, intermediate asymptotics and large-time behaviour of type II Streater's models
    Adv. Differential Equations 6 (4) (2001), 461-480.

  47. P. Biler, G. Karch & W. A. Woyczynski
    Asymptotics and high-dimensional approximations for nonlinear pseudodifferential equations involving Lévy generators
    Demonstratio Math. 34 (2) (2001), 403-413.

  48. Piotr Biler, Grzegorz Karch & Wojbor A. Woyczynski
    Asymptotics for conservation laws involving Lévy diffusion generators
    Studia Math. 148 (2) (2001), 171-192.
    http://dx.doi.org/10.4064/sm148-2-5

  49. Piotr Biler, Grzegorz Karch & Wojbor A. Woyczynski
    Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws
    Ann. Inst. H. Poincaré Anal. Non Linéaire 18 (5) (2001), 613-637.
    http://dx.doi.org/10.1016/S0294-1449(01)00080-4

  50. Marco Cannone & Grzegorz Karch
    Incompressible Navier-Stokes equations in abstract Banach spaces
    Sűrikaisekikenkyűsho K&omacro;kyűroku (1234) (2001), 27-41.
    Tosio Kato's method and principle for evolution equations in mathematical physics (Sapporo, 2001).

  51. Grzegorz Karch
    Scaling in nonlinear parabolic equations: applications to Debye system.
    Disordered and complex systems (London, 2000), 243-248, AIP Conf. Proc. 553, Amer. Inst. Phys., Melville, NY, 2001.
    http://dx.doi.org/10.1063/1.1358191

  52. Piotr Biler & Grzegorz Karch
    A Neumann problem for a convection-diffusion equation on the half-line
    Ann. Polon. Math. 74 (2000), 79-95.
    Dedicated to the memory of Bogdan Ziemian.

  53. Piotr Biler, Grzegorz Karch & Wojbor A. Woyczynski
    Multifractal and Lévy conservation laws
    C. R. Acad. Sci. Paris Sér. I Math. 330 (5) (2000), 343-348.
    http://dx.doi.org/10.1016/S0764-4442(00)00187-7

  54. G. Karch
    Asymptotics of solutions to a convection-diffusion equation on the half-line
    Proc. Roy. Soc. Edinburgh Sect. A 130 (4) (2000), 837-853.
    http://dx.doi.org/10.1017/S0308210500000469

  55. Grzegorz Karch
    Long-time asymptotics of solutions to some nonlinear wave equations.
    Evolution equations: existence, regularity and singularities (Warsaw, 1998), 133-146, Banach Center Publ. 52, Polish Acad. Sci. Inst. Math., Warsaw, 2000.

  56. Grzegorz Karch
    Selfsimilar profiles in large time asymptotics of solutions to damped wave equations
    Studia Math. 143 (2) (2000), 175-197.

  57. Piotr Biler, Grzegorz Karch & Wojbor A. Woyczynski
    Asymptotics for multifractal conservation laws
    Studia Math. 135 (3) (1999), 231-252.

  58. Grzegorz Karch
    Large-time behaviour of solutions to non-linear wave equations: higher-order asymptotics
    Math. Methods Appl. Sci. 22 (18) (1999), 1671-1697.
    http://dx.doi.org/10.1002/(SICI)1099-1476(199912)22:18<1671::AID-MMA98>3.0.CO;2-Q

  59. Grzegorz Karch
    Scaling in nonlinear parabolic equations
    J. Math. Anal. Appl. 234 (2) (1999), 534-558.
    http://dx.doi.org/10.1006/jmaa.1999.6370

  60. Grzegorz Karch
    Self-similar large time behavior of solutions to Korteweg-de Vries-Burgers equation
    Nonlinear Anal. 35 (2, Ser. A: Theory Methods) (1999), 199-219.
    http://dx.doi.org/10.1016/S0362-546X(97)00708-6

  61. Grzegorz Karch
    Asymptotic behaviour of solutions to some pseudoparabolic equations
    Math. Methods Appl. Sci. 20 (3) (1997), 271-289.
    http://dx.doi.org/10.1002/(SICI)1099-1476(199702)20:3<271::AID-MMA859>3.3.CO;2-6

  62. Grzegorz Karch
    L^p-decay of solutions to dissipative-dispersive perturbations of conservation laws
    Ann. Polon. Math. 67 (1) (1997), 65-86.

  63. Grzegorz Karch & Tonia Ricciardi
    Note on Lorentz spaces and differentiability of weak solutions to elliptic equations
    Bull. Polish Acad. Sci. Math. 45 (1) (1997), 111-116.

  64. Jacek Dziubaʼnski & Grzegorz Karch
    Nonlinear scattering for some dispersive equations generalizing Benjamin-Bona-Mahony equation
    Monatsh. Math. 122 (1) (1996), 35-43.
    http://dx.doi.org/10.1007/BF01298454

 
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