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Information on the principal investigator and host institution

Information of the project and the call

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Rigorous numerics for dissipative PDEs and delay equations

2011/03/B/ST1/04780

Keywords:

dissipative PDEs delay equations computer assisted proof dynamics

Descriptors:

  • ST1_16: Numerical analysis
  • ST1_11: Partial differential equations

Panel:

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

Host institution :

Wyższa Szkoła Biznesu - National-Louis University z siedzibą w Nowym Sączu, Wydział Nauk Społecznych 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: 5

Call: OPUS 2 - announced on 2011-09-15

Amount awarded: 231 380 PLN

Project start date (Y-m-d): 2012-08-07

Project end date (Y-m-d): 2015-08-06

Project duration:: 36 months (the same as in the proposal)

Project status: Project settled

Information in the final report

  • Publication in academic press/journals (9)
  1. Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation
    Authors:
    Robert Szczelina i Piotr Zgliczyński
    Academic press:
    Foundatations 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
  2. Rigorous numerics for PDEs with indefinite tail: existence of a periodic solution of the Boussinesq equation with time-dependent forcing
    Authors:
    Aleksander Czechowski, Piotr Zgliczyński
    Academic press:
    Schedae Informaticae (rok: 2015, tom: 24, strony: 143--158), Wydawca: Uniwersytet Jagielloński
    Status:
    Published
    DOI:
    10.4467/20838476SI.15.014.3486 - link to the publication
  3. Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
    Authors:
    Jacek Cyranka, Piotr Zgliczynski
    Academic press:
    Journal of Differential Equations (rok: 2016, tom: 261, strony: 4648--4708), Wydawca: ACADEMIC PRESS INC ELSEVIER SCIENCE
    Status:
    Published
    DOI:
    10.1016/j.jde.2016.07.007 - link to the publication
  4. Stabilizing effect of large average initial velocity in forced dissipative PDEs invariant with respect to Galilean transformations
    Authors:
    Jacek Cyranka i Piotr Zgliczynski
    Academic press:
    Journal of Differential Equations (rok: 2016, tom: 261, strony: 4648--4708), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jde.2016.07.007 - link to the publication
  5. 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
  6. Stabilizing the Long-time Behavior of the Navier-Stokes Equations and Damped Euler Systems by Large Mean Flow
    Authors:
    Jacek Cyranka, Piotr B Mucha, Edriss S Titi, Piotr Zgliczyński
    Academic press:
    Physica D (rok: 2018, tom: 369, strony: 18–-29), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.physd.2017.12.010 - link to the publication
  7. Connecting Orbits for a Singular Nonautonomous Real Ginzburg-Landau Type Equation
    Authors:
    Daniel Wilczak, Piotr Zgliczyński
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2016, tom: 15, strony: 495-525), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/15M1015558 - link to the publication
  8. Existence of Periodic Solutions of the FitzHugh-Nagumo Equations for An Explicit Range of the Small Parameter
    Authors:
    Aleksander Czechowski, Piotr Zgliczynski
    Academic press:
    SIAM Journal on Applied Dynamical Systems (rok: 2016, tom: 15, strony: 1615–1655), Wydawca: SIAM Publications
    Status:
    Published
    DOI:
    10.1137/15M1007707 - link to the publication
  9. Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof
    Authors:
    Jacek Cyranka, Piotr Zgliczyński
    Academic press:
    SIAM Journal of Applied Dynamical Systems (rok: 2015, tom: 14, strony: 787--821), Wydawca: SIAM
    Status:
    Published
    DOI:
    10.1137/14096699X - link to the publication

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