Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

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Geometric methods and computer assisted proofs in dynamics of partial diffential equations

2016/22/A/ST1/00077

Keywords:

dynamics dissipative PDEs rigorous numerics computer assisted proofs geometric methods

Descriptors:

  • ST1_11:
  • ST1_16:
  • ST1_10:

Panel:

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

Host institution :

Uniwersytet Jagielloński, Wydział Matematyki i Informatyki

woj. małopolskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

prof. Piotr Zgliczyński 

Number of co-investigators in the project: 7

Call: MAESTRO 8 - announced on 2016-06-15

Amount awarded: 1 758 900 PLN

Project start date (Y-m-d): 2017-04-18

Project end date (Y-m-d): 2024-04-17

Project duration:: 84 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.

Information in the final report

  • Publication in academic press/journals (35)
  • Book publications / chapters in book publications (1)
  1. RAYLEIGH- BÉNARD PROBLEM FOR THERMOMICROPOLAR FLUIDS
    Authors:
    PIOTR KALITA, GRZEGORZ ŁUKASZEWICZ, AND JAKUB SIEMIANOWSKI
    Academic press:
    Topological Methods in Nonlinear Analysis (rok: 2018, tom: 52, strony: 477-514), Wydawca: Juliusz Schauder Center
    Status:
    Published
    DOI:
    10.12775/TMNA.2018.012 - link to the publication
  2. Rigorous FEM for 1D Burgers Equation
    Authors:
    Piotr Kalita, Piotr Zgliczyński
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2021, tom: 20(2), strony: 853–907), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/20M1338216 - link to the publication
  3. On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions
    Authors:
    P. Kalita, P. Zgliczyński
    Academic press:
    Proc. A Royal Soc. Edinburgh (rok: 2020, tom: 150, strony: 2025-2054), Wydawca: CAMBRIDGE UNIV PRESS
    Status:
    Published
    DOI:
    10.1017/prm.2019.11 - link to the publication
  4. Recent advances in rigorous computation of Poincare maps
    Authors:
    Tomasz Kapela, Daniel Wilczak, Piotr Zgliczyński
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2022, tom: 110, strony: 106366), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2022.106366 - link to the publication
  5. Long-time behavior for impulsive generalized semiflows
    Authors:
    Piotr Kalita, Everaldo de Mello Bonotto
    Academic press:
    Nonlinear Analysis-Hybrid Systems (rok: 2024, tom: 51, strony: 45682), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.nahs.2023.101432 - link to the publication
  6. Forwards attractor structures in a planar cooperative non-autonomous Lotka-Volterra system
    Authors:
    Juan Garcia-Fuentes, Piotr Kalita, Jose A. Langa
    Academic press:
    Qualitative Theory of Dynamical Systems (rok: 2023, tom: vol. 23, strony: article number 163), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12346-024-01020-0 - link to the publication
  7. Vertical heat transport at infinite Prandtl number for micropolar fluid
    Authors:
    M. Caggio, P. Kalita, G. Łukaszewicz, K. Mizerski
    Academic press:
    Archives of Mechanics (rok: 2020, tom: 72, strony: 525-553), Wydawca: IPPT PAN
    Status:
    Published
    DOI:
    10.24423/aom.3598 - link to the publication
  8. On renormalized solutions to elliptic inclusions with nonstandard growth
    Authors:
    Anna Denkowska, Piotr Gwiazda, Piotr Kalita
    Academic press:
    Calculus of Variations and Partial Differential Equations (rok: 2021, tom: 60, strony: 21), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00526-020-01893-4 - link to the publication
  9. Structural stability of invasion graphs for Lotka-Volterra systems
    Authors:
    Pablo Almaraz, Piotr Kalita, Jose A. Langa, Fernando Soler-Toscano
    Academic press:
    Journal of Mathematical Biology (rok: 2024, tom: vol. 88 article number 64, strony: 45682), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00285-024-02087-8 - link to the publication
  10. On maximal attractors for dynamical systems. Application to a semilinear parabolic problem with controlled growth
    Authors:
    Matheus Cheque Bortolan, Juliana Fernandes, Juan Garcia-Fuentes, Piotr Kalita
    Academic press:
    Journal of Evolution Equations (rok: 2024, tom: 24, strony: 45681), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00028-024-00966-7 - link to the publication
  11. Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation
    Authors:
    Robert Szczelina, Piotr Zgliczyński
    Academic press:
    Foundations of Computational Mathematics (rok: 2018, tom: 18, strony: 1299–1332), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10208-017-9369-5 - link to the publication
  12. Informational Structures and Informational Fields as a prototype for the description of postulates of the Integrated Information Theory
    Authors:
    Piotr Kalita, Jose Antonio Langa, Fernando Soler-Toscano
    Academic press:
    Entropy (rok: 2019, tom: 21(5):493, strony: 45678), Wydawca: MDPI
    Status:
    Published
    DOI:
    10.3390/e21050493 - link to the publication
  13. A geometric method for infinite-dimensional chaos: Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line
    Authors:
    Daniel Wilczak, Piotr Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2020, tom: 269, strony: 8509-8548), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2020.06.020 - link to the publication
  14. A frictional contact problem with wear diffusion
    Authors:
    Piotr Kalita, Pawel Szafraniec, Meir Shillor
    Academic press:
    Zeitschrift für angewandte Mathematik und Physik (rok: 2019, tom: 70, strony: 45674), Wydawca: SPRINGER
    Status:
    Published
    DOI:
    10.1007/s00033-019-1141-z - link to the publication
  15. Autonomous and Non-autonomous Unbounded Attractors in Evolutionary Problems
    Authors:
    J. Banaśkiewicz, A. Nolasco de Carvalho, J. Garcia-Fuentes, P. Kalita
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2023, tom: 1, strony: 19725), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10239-x - link to the publication
  16. From the Sharkovskii theorem to periodic orbits for the Rossler system
    Authors:
    A. Gierzkiewicz, P. Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2022, tom: 314, strony: 733-751), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2022.01.022 - link to the publication
  17. On multivalued Duffing equation
    Authors:
    Piotr Kalita, Piotr M Kowalski
    Academic press:
    Journal of Mathematical Analysis and Applications (rok: 2018, tom: 462, strony: 1130-1147), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2018.01.067 - link to the publication
  18. Micropolar meets Newtonian. The Rayleigh–Bénard problem
    Authors:
    P. Kalita, G. Łukaszewicz, J.A. Langa
    Academic press:
    Physica D (rok: 2019, tom: 392, strony: 57-80), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physd.2018.12.004 - link to the publication
  19. ON ATTRACTORS OF GENERALIZED SEMIFLOWS WITH IMPULSES
    Authors:
    EVERALDO DE MELLO BONOTTO, PIOTR KALITA
    Academic press:
    Journal of Geometric Analysis (rok: 2020, tom: 30, strony: 1412-1449), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s12220-019-00143-0 - link to the publication
  20. Micropolar meets Newtonian in 3D. The Rayleigh--Bénard problem for large Prandtl numbers
    Authors:
    Piotr Kalita, Grzegorz Łukaszewicz
    Academic press:
    Nonlinearity (rok: 2020, tom: 33, strony: 5686), Wydawca: IOPscience
    Status:
    Published
    DOI:
    10.1088/1361-6544/ab9729 - link to the publication
  21. Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations
    Authors:
    Mirelson M. Freitas, Piotr Kalita, Jose A .Langa
    Academic press:
    Journal of Differential Equations (rok: 2018, tom: 264, strony: 1886–1945), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.007 - link to the publication
  22. Autonomous and non-autonomous unbounded attractors in evolutionary problems
    Authors:
    Jakub Banaśkiewicz, Alexandre Nolasco de Carvalho, Juan Garcia-Fuentes, Piotr Kalita
    Academic press:
    Journal of Dynamics and Differential Equations (rok: 2022, tom: Early Access, strony: 19725), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s10884-022-10239-x - link to the publication
  23. Periodic orbits in Rossler system
    Authors:
    A. Gierzkiewicz, P. Zgliczynski
    Academic press:
    Communications in Nonlinear Science and Numerical Simulation (rok: 2021, tom: 101, strony: 45670), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.cnsns.2021.105891 - link to the publication
  24. Convergence of non-autonomous attractors for subquintic weakly damped wave equation
    Authors:
    Jakub Banaśkiewicz, Piotr Kalita
    Academic press:
    Applied Mathematics and Optimization (rok: 2021, tom: 84, strony: 943-978), Wydawca: Springer
    Status:
    Published
    DOI:
    10.1007/s00245-021-09790-8 - link to the publication
  25. Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions
    Authors:
    Maciej J. Capinski, Hubert Kubica
    Academic press:
    Nonlinearity (rok: 2020, tom: 33, strony: 4967–5005), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1361-6544/ab8fb6 - link to the publication
  26. On relation between attractors for single and multivalued semiflows for a certain class of PDEs
    Authors:
    Piotr Kalita, Grzegorz Łukaszewicz, Jakub Siemianowski
    Academic press:
    Discrete and Continuous Dynamical System Series B (rok: 2019, tom: 24, strony: 1199-1227), Wydawca: American Institute of Mathematical Sciences
    Status:
    Published
    DOI:
    10.3934/dcdsb.2019012 - link to the publication
  27. On dynamic contact problem with generalized Coulomb friction, normal compliance and damage
    Authors:
    Leszek Gasiński, Piotr Kalita
    Academic press:
    Evolution Equations and Control Theory (rok: 2020, tom: 9, strony: 1009-1026), Wydawca: AIMS
    Status:
    Published
    DOI:
    10.3934/eect.2020049 - link to the publication
  28. Shadowing of non-transversal heteroclinic chains
    Authors:
    Amadeu Delshams, Adria Simon, Piotr Zgliczyński
    Academic press:
    Journal of Differential Equations (rok: 2018, tom: 264, strony: 3619–-3663), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2017.11.024 - link to the publication
  29. Persistence of normally hyperbolic invariant manifolds in the absence of rate conditions
    Authors:
    Maciej J. Capinski, Hubert Kubica
    Academic press:
    Nonlinearity (rok: 2020, tom: 33, strony: 4967–5005), Wydawca: IOP
    Status:
    Published
    DOI:
    10.1088/1361-6544/ab8fb6 - link to the publication
  30. Micropolar meets Newtonian. The Rayleigh–Bénard problem
    Authors:
    P. Kalita, G. Łukaszewicz, J.A. Langa
    Academic press:
    Physica D (rok: 2019, tom: 392, strony: 57-80), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physd.2018.12.004 - link to the publication
  31. High-order Lohner-type algorithm for rigorous computation of Poincare maps in systems of Delay Differential Equations with several delays
    Authors:
    R. Szczelina, P. Zgliczyński
    Status:
    Accepted for publication
  32. Forwards attractors for non-autonomous Lotka-Volterra cooperative systems: a detailed geometrical description,
    Authors:
    Juan Garcia-Fuentes, Piotr Kalita, Jose A. Langa, Antonio Suarez
    Status:
    Accepted for publication
  33. Computer-assisted validation of the existence of periodic orbit in the Brusselator system
    Authors:
    J. Banaśkiewicz, P. Kalita, P. Zgliczyński
    Status:
    Accepted for publication
  34. Computer-assisted validation of the existence of periodic orbit in the Brusselator system
    Authors:
    Jakub Banaśkiewicz, Piotr Kalita, Piotr Zgliczyński
    Status:
    Accepted for publication
  35. Forwards attractors for non-autonomous Lotka-Volterra cooperative systems: a detailed geometrical description,
    Authors:
    Juan Garcia-Fuentes, Piotr Kalita, Jose A. Langa, Antonio Suarez
    Status:
    Accepted for publication
  1. Nonlinear Semigroups and Their Perturbations in Hydrodynamics. Three Examples
    Authors:
    Piotr Kalita, Grzegorz Łukaszewicz, Jakub Siemianowski
    Book:
    Semigroups of Operators – Theory and Applications (rok: 2020, tom: 325, strony: 227-250), Wydawca: Springer
    Status:
    Published

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