Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

Equipment

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Nonlocal parabolic problems: regularity, blowup, pattern formation

2016/23/B/ST1/00434

Keywords:

chemotaxis quasilinear parabolic problems regularity of solutions porous media equation pattern formation

Descriptors:

  • ST1_11: Partial differential equations
  • ST1_8: Analysis
  • 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. Piotr Biler 

Number of co-investigators in the project: 6

Call: OPUS 12 - announced on 2016-09-15

Amount awarded: 505 150 PLN

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

Project end date (Y-m-d): 2022-07-17

Project duration:: 60 months (the same as in the proposal)

Project status: Project settled

Project description

Download the project description in a pdf file

Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Equipment purchased [PL]

  1. komputer przenośny (2 szt.) (10 000 PLN)
  2. Laptop Dell XPS 13 7390.
  3. skaner (500 PLN)

Information in the final report

  • Publication in academic press/journals (23)
  • Book publications / chapters in book publications (1)
  1. Blowing up radial solutions in the minimal Keller-Segel model of chemotaxis
    Authors:
    Piotr Biler, Jacek Zienkiewicz
    Academic press:
    J. Evol. Equ. (rok: 2019, tom: 19, strony: 71-90), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00028-018-0469-8 - link to the publication
  2. Concentration phenomena in a diffusive aggregation model
    Authors:
    Piotr Biler, Alexandre Boritchev, Grzegorz Karch, Philippe Laurençot
    Academic press:
    J. Differential Equations (rok: 2021, tom: 271, strony: 1092–1108), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2020.09.035 - 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. Mathematical challenges in the theory of chemotaxis
    Authors:
    Piotr Biler
    Academic press:
    Ann. Math. Silesianae (rok: 2018, tom: 32, strony: 43-63), Wydawca: De Gruyter
    Status:
    Published
    DOI:
    10.2478/amsil-2018-0004 - link to the publication
  5. Pattern formation in nonlocal Kondo model
    Authors:
    Szymon Cygan
    Academic press:
    Math. Methods Appl. Sci. (rok: 2021, tom: 44, strony: 10804-10822), Wydawca: Wiley
    Status:
    Published
    DOI:
    10.1002/mma.7448 - link to the publication
  6. On fully nonlinear parabolic mean field games with examples of nonlocal and local diffusions
    Authors:
    Indranil Chowdhury, Espen R. Jakobsen, Miłosz Krupski
    Academic press:
    J. Math. Pures. Appl. , Wydawca: elsevier
    Status:
    Submitted
    DOI:
    brak - link to the publication
  7. A framework for nonlocal, nonlinear initial value problems
    Authors:
    Grzegorz Karch, Moritz Kassmann, Miłosz Krupski
    Academic press:
    SIAM J. Mathematical Analysis (rok: 2020, tom: 52, strony: 2383-2410), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/19M124143X - link to the publication
  8. Around a singular solution of a nonlocal nonlinear heat equation
    Authors:
    Piotr Biler, Dominika Pilarczyk
    Academic press:
    NoDEA, Nonlinear Differ. Equ. Appl. (rok: 2019, tom: 26, strony: 5:1-24), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00030-019-0552-z - link to the publication
  9. Discontinuous stationary solutions to certain reaction-diffusion systems
    Authors:
    Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch
    Academic press:
    Partial Differential Equations and Applications (rok: 2022, tom: 3, strony: 1-15, 3:49), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s42985-022-00188-x - link to the publication
  10. Asymptotic profile of solutions to a certain chemotaxis system
    Authors:
    Rafał Celiński, Andrzej Raczyński
    Academic press:
    Comm. Pure Applied Analysis (rok: 2020, tom: 19, strony: 911-922), Wydawca: Amer. Inst. Math. Sciences
    Status:
    Published
    DOI:
    10.3934/cpaa.2020041 - link to the publication
  11. Blowup of solutions for nonlinear nonlocal heat equation
    Authors:
    Piotr Biler
    Academic press:
    Monatsh. Math. (rok: 2019, tom: 189, strony: 611-624), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00605-019-01269-7 - link to the publication
  12. Convection-diffusion equations with random initial conditions
    Authors:
    Miłosz Krupski
    Academic press:
    J. Math. Anal. Appl. (rok: 2018, tom: 470, strony: 1194-1221), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.060 - link to the publication
  13. Instability of all regular stationary solutions to reaction-diffusion-ode systems
    Authors:
    Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
    Academic press:
    J. Differential Equations (rok: 2022, tom: 337, strony: 460-482), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2022.08.007 - link to the publication
  14. Large global solutions of the parabolic-parabolic Keller–Segel system in higher dimensions
    Authors:
    Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese
    Academic press:
    J. Differential Equations (rok: 2023, tom: 344, strony: 891-914), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2022.11.018 - link to the publication
  15. Stability of constant steady states of a chemotaxis model
    Authors:
    Szymon Cygan, Grzegorz Karch, Krzysztof Krawczyk, Hiroshi Wakui
    Academic press:
    J. Evolution Equations (rok: 2021, tom: 21, strony: 4873-4896), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00028-021-00735-w - link to the publication
  16. 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, strony: 147-160), Wydawca: Centrum Badań Nieliniowych, UMK
    Status:
    Published
    DOI:
    10.12775/TMNA.2018.013 - link to the publication
  17. Existence of solutions to a one-dimensional Hamilton-Jacobi equation with a degenerate Hamiltonian
    Authors:
    Tomasz Cieślak, Hiroshi Wakui
    Academic press:
    Applicationes Mathematicae (rok: 2020, tom: 47, strony: 155-163), Wydawca: Instytut Matematyczny PAN
    Status:
    Published
    DOI:
    10.4064/am2407-7-2020 - link to the publication
  18. Global radial solutions in classical Keller–Segel model of chemotaxis
    Authors:
    Piotr Biler, Grzegorz Karch, Dominika Pilarczyk
    Academic press:
    J. Differential Equations (rok: 2019, tom: 267, strony: 6352-6369), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2019.06.024 - link to the publication
  19. Large self-similar solutions of the parabolic-elliptic Keller-Segel model
    Authors:
    Piotr Biler, Grzegorz Karch, Hiroshi Wakui
    Academic press:
    Indiana Univ. Math. J. (rok: 2023, tom: n/a, strony: n/a), Wydawca: Indiana University
    Status:
    Accepted for publication
    DOI:
    n/a - link to the publication
  20. Sharp well-posedness and blowup results for parabolic systems of the Keller–Segel type
    Authors:
    Piotr Biler, Alexandre Boritchev, Lorenzo Brandolese
    Academic press:
    Annales de la Faculte de Sciences de Toulouse , Wydawca: Centre Mersenne for open scientific publishing
    Status:
    Submitted
    DOI:
    brak - link to the publication
  21. Stable discontinuous stationary solutions to reaction-diffusion-ode systems
    Authors:
    Szymon Cygan, Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
    Academic press:
    Communications in Partial Differential Equations , Wydawca: Taylor and francis
    Status:
    Submitted
    DOI:
    brak - link to the publication
  22. Regular solutions to the fractional Euler alignment system in the Besov spaces framework
    Authors:
    Raphaël Danchin, Piotr B. Mucha, Jan Peszek, Bartosz Wróblewski
    Academic press:
    Mathematical Models and Methods in Applied Sciences (rok: 2019, tom: 29, strony: 89-119), Wydawca: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0218202519500040 - link to the publication
  23. Sharp Sobolev estimates for concentration of solutions to an aggregation-diffusion equation
    Authors:
    Piotr Biler, Alexander Boritchev, Grzegorz Karch,Philippe Laurencot
    Academic press:
    J. Dynamics Differential Equations (rok: 2022, tom: 34, strony: 3431-3441), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-021-09998-w - link to the publication
  1. De Gruyter Series in Mathematics and Life Sciences; ISBN 978-3-11-059789-9
    Authors:
    Piotr Biler
    Book:
    Singularities of Solutions to Chemotaxis Systems (rok: 2020, tom: 6, strony: i-xxiv, 1-207), Wydawca: Walter DeGruyter
    Status:
    Published

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