Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Singularities and asymptotic profiles in nonlocal models

2013/09/B/ST1/04412

Keywords:

reaction-diffusion equations homogeneous Boltzmann equation chemotaxis system dislocations nonlocal operators

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_12: Mathematical methods of physics
  • ST1_18: Control theory and optimisation

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

woj. 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 (Y-m-d): 2014-02-19

Project end date (Y-m-d): 2017-07-18

Project duration:: 41 months (the same as in the proposal)

Project status: Project settled

Equipment purchased [PL]

  1. Notebook (5 000 PLN)

Information in the final report

  • Publication in academic press/journals (18)
  1. 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 (rok: 2016, tom: 29 (7-8), strony: 715-730), Wydawca: Khayyam Publishing
    Status:
    Published
    DOI:
    brak - link to the publication
  2. Dynamical spike solutions in a nonlocal model of pattern formation
    Authors:
    Anna Marciniak-Czochra, Steffen Härting, Grzegorz Karch, Kanako Suzuki
    Academic press:
    NONLINEARITY (rok: 2018, tom: 31, no. 5, strony: 1757-1781), Wydawca: IOP Publishing Ltd & London Mathematical Society
    Status:
    Published
    DOI:
    10.1088/1361-6544/aaa5dc - link to the publication
  3. Large global-in-time solutions to a nonlocal model of chemotaxis
    Authors:
    Piotr Biler, Grzegorz Karch, Jacek Zienkiewicz
    Academic press:
    ADVANCES IN MATHEMATICS (rok: 2018, tom: 330, strony: 834-875), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2018.03.036 - link to the publication
  4. Optimal criteria for blowup of radial and N-symmetric solutions of chemotaxis systems
    Authors:
    Piotr Biler, Grzegorz Karch and Jacek Zienkiewicz
    Academic press:
    Nonlinearity (rok: 2015, tom: 28, strony: 4369–4387), Wydawca: IOP Publishing, London Mathematical Society
    Status:
    Published
    DOI:
    10.1088/0951-7715/28/12/4369 - link to the publication
  5. 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. (rok: 2015, tom: 63, strony: 41-51), Wydawca: Polish Acad. Sci.
    Status:
    Published
    DOI:
    10.4064/ba63-1-6 - link to the publication
  6. GLOBAL WELL-POSEDNESS FOR THE TWO-DIMENSIONAL INCOMPRESSIBLE CHEMOTAXIS-NAVIER–STOKES EQUATIONS
    Authors:
    QIAN ZHANG AND XIAOXIN ZHENG
    Academic press:
    SIAM J. MATH. ANAL. (rok: 2014, tom: 46, strony: 3078-3105), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/130936920 - link to the publication
  7. 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 (rok: 2015, tom: 14(6), strony: 2117-2126), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/cpaa.2015.14.2117 - 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 (rok: 2017, tom: 17, strony: 1750019 (24 pages)), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219493717500198 - link to the publication
  9. 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. (rok: 2017, tom: (9) 108, strony: 14–40.), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.008 - link to the publication
  10. Local criteria for blowup in two-dimensional chemotaxis models.
    Authors:
    Biler, Piotr; Cieślak, Tomasz; Karch, Grzegorz; Zienkiewicz, Jacek
    Academic press:
    Discrete Contin. Dyn. Syst. (rok: 2017, tom: 37, strony: 1841–1856), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcds.2017077 - link to the publication
  11. TIME-DEPENDENT SINGULARITIES IN THE NAVIER-STOKES SYSTEM
    Authors:
    Grzegorz Karch and Xiaoxin Zheng
    Academic press:
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS (rok: 2015, tom: 35 (7), strony: 3039-3057), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/dcds.2015.35.3039 - link to the publication
  12. The Nonlocal Porous Medium Equation: Barenblatt Profiles and Other Weak Solutions
    Authors:
    Piotr Biler, Cyril Imbert & Grzegorz Karch
    Academic press:
    Arch. Rational Mech. Anal. (rok: 2015, tom: 215, strony: 497–529), Wydawca: Spring Verlag
    Status:
    Published
    DOI:
    10.1007/s00205-014-0786-1 - link to the publication
  13. Finite-time blowup of solutions to some activator-inhibitor systems
    Authors:
    Grzegorz Karch, Kanako Suzuki & Jacek Zienkiewicz
    Academic press:
    Discrete Contin. Dyn. Syst. (rok: 2016, tom: 36 (9), strony: 4997-5010), Wydawca: American Institute of Applied Sciences
    Status:
    Published
    DOI:
    10.3934/dcds.2016016 - link to the publication
  14. MORREY SPACES NORMS AND CRITERIA FOR BLOWUP IN CHEMOTAXIS MODELS
    Authors:
    Piotr Biler, Grzegorz Karch and Jacek Zienkiewicz
    Academic press:
    NETWORKS AND HETEROGENEOUS MEDIA (rok: 2016, tom: 11(2), strony: 239-250), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/nhm.2016.11.239 - link to the publication
  15. 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 (rok: 2015, tom: 38, strony: 2830-2839), Wydawca: John Wiley & Sons, Ltd.
    Status:
    Published
    DOI:
    10.1002/mma.3266 - link to the publication
  16. Asymptotics of solutions to the Navier–Stokes system in exterior domains
    Authors:
    Dragoş Iftimie, Grzegorz Karch, Christophe Lacave
    Academic press:
    J. London Math. Soc. (rok: 2014, tom: 90, strony: 785–806), Wydawca: Oxford Univ. Press
    Status:
    Published
    DOI:
    10.1112/jlms/jdu052 - link to the publication
  17. Blowup versus global in time existence of solutions for nonlinear heat equations
    Authors:
    Piotr Biler
    Academic press:
    Topol. Meth. Nonlinear Anal. (rok: 2018, tom: 52(1), strony: 147-160), Wydawca: Juliusz Schauder University Centre for Nonlinear Studies
    Status:
    Published
    DOI:
    10.12775/TMNA.2018.013 - link to the publication
  18. Instability of Turing patterns in reaction-diffusion-ODE systems
    Authors:
    Anna Marciniak-Czochra, Grzegorz Karch & Kanako Suzuki
    Academic press:
    J. Math. Biol. (rok: 2017, tom: 74 (3), strony: 583-618), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00285-016-1035-z - link to the publication

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