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Singularities and asymptotic profiles in nonlocal models

2013/09/B/ST1/04412

Keywords

Descriptors

  • ST1_11: Równania różniczkowe cząstkowe
  • ST1_12: Fizyka matematyczna
  • ST1_18: Zastosowania matematyki w innych naukach

Panel

ST1 – Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution

Uniwersytet Wrocławski, Wydział Matematyki i Informatyki

Voivodeship: dolnośląskie

Other projects carried out by the institution »

Principal investigator (from the host institution)

prof. Grzegorz Karch

Number of co-investigators in the project: 6

Call

OPUS 5 – announced on 2013-03-15

Amount awarded
457 260 PLN
Project start date
2014-02-19
Project end date
2017-07-18
Project duration
41 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

  1. Notebook. Cost: 5 000 PLN

Information in the final report

Publication in academic press/journals (18)

  1. The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions

    Authors:
    Piotr Biler, Cyril Imbert & Grzegorz Karch
    Academic press:
    Arch. Rational Mech. Anal. (year: 2015, volume: 215, pages: 497–529), Publisher: Spring Verlag
    Status:
    Published
    DOI:
    10.1007/s00205-014-0786-1 – link to the publication

  2. Optimal criteria for blowup of radial and N-symmetric solutions of chemotaxis systems

    Authors:
    Piotr Biler, Grzegorz Karch and Jacek Zienkiewicz
    Academic press:
    Nonlinearity (year: 2015, volume: 28, pages: 4369–4387), Publisher: IOP Publishing, London Mathematical Society
    Status:
    Published
    DOI:
    10.1088/0951-7715/28/12/4369 – link to the publication

  3. Asymptotics of solutions to the Navier–Stokes system in exterior domains

    Authors:
    Dragoş Iftimie, Grzegorz Karch, Christophe Lacave
    Academic press:
    J. London Math. Soc. (year: 2014, volume: 90, pages: 785–806), Publisher: Oxford Univ. Press
    Status:
    Published
    DOI:
    10.1112/jlms/jdu052 – link to the publication

  4. Local criteria for blowup in two-dimensional chemotaxis models.

    Authors:
    Biler, Piotr; Cieślak, Tomasz; Karch, Grzegorz; Zienkiewicz, Jacek
    Academic press:
    Discrete Contin. Dyn. Syst. (year: 2017, volume: 37, pages: 1841–1856), Publisher: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcds.2017077 – link to the publication

  5. Blowup versus global in time existence of solutions for nonlinear heat equations

    Authors:
    Piotr Biler
    Academic press:
    Topol. Meth. Nonlinear Anal. (year: 2018, volume: 52(1), pages: 147-160), Publisher: Juliusz Schauder University Centre for Nonlinear Studies
    Status:
    Published
    DOI:
    10.12775/TMNA.2018.013 – link to the publication

  6. LARGE GLOBAL-IN-TIME SOLUTIONS OF THE PARABOLIC-PARABOLIC KELLER-SEGEL SYSTEM ON THE PLANE

    Authors:
    P. Biler, I. Guerra, G. Karch
    Academic press:
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (year: 2015, volume: 14(6), pages: 2117-2126), Publisher: AIMS
    Status:
    Published
    DOI:
    10.3934/cpaa.2015.14.2117 – link to the publication

  7. Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data

    Authors:
    Piotr Biler, Jacek Zienkiewicz
    Academic press:
    Bull. Pol. Ac. Sci., Math. (year: 2015, volume: 63, pages: 41-51), Publisher: Polish Acad. Sci.
    Status:
    Published
    DOI:
    10.4064/ba63-1-6 – link to the publication

  8. Scaling limits of solutions of linear evolution equations with random initial conditions

    Authors:
    Miłosz Krupski
    Academic press:
    Stochastics and Dynamics (year: 2017, volume: 17, pages: 1750019 (24 pages)), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219493717500198 – link to the publication

  9. Large global-in-time solutions to a nonlocal model of chemotaxis

    Authors:
    Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
    Academic press:
    ADVANCES IN MATHEMATICS (year: 2018, volume: 330, pages: 834-875), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2018.03.036 – link to the publication

  10. Dynamical spike solutions in a nonlocal model of pattern formation

    Authors:
    Anna Marciniak-Czochra, Steffen Härting, Grzegorz Karch, Kanako Suzuki
    Academic press:
    NONLINEARITY (year: 2018, volume: 31, no. 5, pages: 1757-1781), Publisher: IOP Publishing Ltd & London Mathematical Society
    Status:
    Published
    DOI:
    10.1088/1361-6544/aaa5dc – link to the publication

  11. MORREY SPACES NORMS AND CRITERIA FOR BLOWUP IN CHEMOTAXIS MODELS

    Authors:
    Piotr Biler, Grzegorz Karch and Jacek Zienkiewicz
    Academic press:
    NETWORKS AND HETEROGENEOUS MEDIA (year: 2016, volume: 11(2), pages: 239-250), Publisher: AIMS
    Status:
    Published
    DOI:
    10.3934/nhm.2016.11.239 – link to the publication

  12. L^2-asymptotic stability of singular solutions to the Navier-Stokes system of equations in R^3.

    Authors:
    Karch, Grzegorz; Pilarczyk, Dominika; Schonbek, Maria E.
    Academic press:
    J. Math. Pures Appl. (year: 2017, volume: (9) 108, pages: 14–40.), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.matpur.2016.10.008 – link to the publication

  13. Instability of Turing patterns in reaction-diffusion-ODE systems

    Authors:
    Anna Marciniak-Czochra, Grzegorz Karch & Kanako Suzuki
    Academic press:
    J. Math. Biol. (year: 2017, volume: 74 (3), pages: 583-618), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00285-016-1035-z – link to the publication

  14. TIME-DEPENDENT SINGULARITIES IN THE NAVIER-STOKES SYSTEM

    Authors:
    Grzegorz Karch and Xiaoxin Zheng
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (year: 2015, volume: 35 (7), pages: 3039-3057), Publisher: AIMS
    Status:
    Published
    DOI:
    10.3934/dcds.2015.35.3039 – link to the publication

  15. GLOBAL WELL-POSEDNESS FOR THE TWO-DIMENSIONAL INCOMPRESSIBLE CHEMOTAXIS-NAVIER–STOKES EQUATIONS

    Authors:
    QIAN ZHANG AND XIAOXIN ZHENG
    Academic press:
    SIAM J. MATH. ANAL. (year: 2014, volume: 46, pages: 3078-3105), Publisher: SIAM
    Status:
    Published
    DOI:
    10.1137/130936920 – link to the publication

  16. Finite-time blowup of solutions to some activator-inhibitor systems

    Authors:
    Grzegorz Karch, Kanako Suzuki & Jacek Zienkiewicz
    Academic press:
    Discrete Contin. Dyn. Syst. (year: 2016, volume: 36 (9), pages: 4997-5010), Publisher: American Institute of Applied Sciences
    Status:
    Published
    DOI:
    10.3934/dcds.2016016 – link to the publication

  17. Two-dimensional fractal Burgers equation with step-like initial conditions

    Authors:
    Grzegorz Karcha, Anna Pudełko and Xiaojing Xu
    Academic press:
    Mathematical Methods in the Applied Sciences (year: 2015, volume: 38, pages: 2830-2839), Publisher: John Wiley & Sons, Ltd.
    Status:
    Published
    DOI:
    10.1002/mma.3266 – link to the publication

  18. Diffusion-driven blowup of nonnegative solutions to reaction-diffusion-ODE systems

    Authors:
    Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki & Jacek Zienkiewicz
    Academic press:
    Differential Integral Equations (year: 2016, volume: 29 (7-8), pages: 715-730), Publisher: Khayyam Publishing
    Status:
    Published

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