2 citations · 3 across the 6 of their papers we have counts for
7 papers
Self-consistent bounds method for dissipative PDEs
Daniel Wilczak, Piotr Zgliczyński
We discuss the method of self-consistent bounds for dissipative PDEs with periodic boundary conditions. We prove convergence theorems for a class of dissipative PDEs, which constit…
Stability of phase portrait for a gradient ODE with memory
Piotr Kalita, Piotr Zgliczyński
We consider the problem governed by the gradient ODE in on which we assume that it has a finite number of hyperbolic equilibria whose stable and uns…
Symbolic dynamics for the Kuramoto-Sivashinsky PDE on the line II
Daniel Wilczak, Piotr Zgliczyński
We prove the existence of infinite number of homoclinic and heteroclinic orbits to two periodic orbits for the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary c…
Pitchfork bifurcation and heteroclinic connections in the Kuramoto--Sivashinsky PDE
Jacek Kubica, Piotr Zgliczyński, Piotr Kalita
We present a method for the complete analysis of the dynamics of dissipative Partial Differential Equations (PDEs) undergoing a pitchfork bifurcation. We apply our technique to the…
Computer-assisted validation of the existence of periodic orbit in the Brusselator system
Jakub Banaśkiewicz, Piotr Kalita, Piotr Zgliczyński
We investigate the Brusselator system with diffusion and Dirichlet boundary conditions on one dimensional space interval. Our proof demonstrates that, for certain parameter values,…
Characterising blenders via covering relations and cone conditions
Maciej J. Capiński, Bernd Krauskopf, Hinke M. Osinga +1
We present a characterisation of a blender based on the topological alignment of certain sets in phase space in combination with cone conditions. Importantly, the required conditio…