22 citations · 49 across the 12 of their papers we have counts for
15 papers
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,…
Forwards attractors for non-autonomous Lotka-Volterra cooperative systems: a detailed geometrical description
Juan Garcia-Fuentes, José A. Langa, Piotr Kalita +1
Non-autonomous differential equations exhibit a highly intricate dynamics, and various concepts have been introduced to describe their qualitative behavior. In general, it is rare…
Autonomous and non-autonomous unbounded attractors in evolutionary problems
Jakub Banaśkiewicz, Alexandre N. Carvalho, Juan Garcia-Fuentes +1
If the semigroup is slowly non-dissipative, i.e., its solutions can diverge to infinity as time tends to infinity, one still can study its dynamics via the approach by the unbounde…
Structural stability of invasion graphs for Lotka--Volterra systems
Pablo Almaraz, Piotr Kalita, José A. Langa +1
In this paper, we study in detail the structure of the global attractor for the Lotka--Volterra system with a Volterra--Lyapunov stable structural matrix. We consider the invasion…
Convergence of non-autonomous attractors for subquintic weakly damped wave equation
Jakub Banaśkiewicz, Piotr Kalita
We study the non-autonomous weakly damped wave equation with subquintic growth condition on the nonlinearity. Our main focus is the class of Shatah--Struwe solutions, which satisfy…
Rigorous FEM for 1D Burgers equation
Piotr Kalita, Piotr Zgliczyński
We propose a method to integrate dissipative PDEs rigorously forward in time with the use of Finite Element Method (FEM). The technique is based on the Galerkin projection on the F…
On renormalized solutions to elliptic inclusions with nonstandard growth
Anna Denkowska, Piotr Gwiazda, Piotr Kalita
We study the elliptic inclusion given in the following divergence form \begin{align*} & -\mathrm{div}\, A(x,\nabla u) \ni f\quad \mathrm{in}\quad Ω, & u=0\quad \mathrm{on}\quad \pa…
Micropolar meets Newtonian in three dimensions. The Rayleigh--B{é}nard problem for large Prandtl numbers
Piotr Kalita, Grzegorz Łukaszewicz
We consider the Rayleigh--Bénard problem for the three--dimensional Boussinesq system for the micropolar fluid. We introduce the notion of the multivalued eventual semiflow and pro…
A frictional contact problem with wear diffusion
Piotr Kalita, Pawel Szafraniec, Meir Shillor
This paper constructs and analyzes a model for the dynamic frictional contact between a viscoelastic body and a moving foundation. The contact involves wear of the contacting surfa…
On non-autonomously forced Burgers equation with periodic and Dirichlet boundary conditions
Piotr Kalita, Piotr Zgliczyński
We study the non-autonomously forced Burgers equation on the space interval with two sets of the boundary conditions:…
Smooth attractors for weak solutions of the SQG equation with critical dissipation
Michele Coti Zelati, Piotr Kalita
We consider the evolution of weak vanishing viscosity solutions to the critically dissipative surface quasi-geostrophic equation. Due to the possible non-uniqueness of solutions, w…
Minimality properties of set-valued processes and their pullback attractors
Michele Coti Zelati, Piotr Kalita
We discuss the existence of pullback attractors for multivalued dynamical systems on metric spaces. Such attractors are shown to exist without any assumptions in terms of continuit…
Semidiscrete variable time-step θ-scheme for nonmonotone evolution inclusion
Piotr Kalita
In this paper we show the convergence of a semidiscrete time stepping θ-scheme on a time grid of variable length to the solution of parabolic operator differential inclusion in the…
Attractors for Navier-Stokes flows with multivalued and nonmonotone subdifferential boundary conditions
P. Kalita, G. Łukaszewicz
We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the e…
Global attractors for multivalued semiflows with weak continuity properties
P. Kalita, G. Łukaszewicz
A method is proposed to deal with some multivalued semiflows with weak continuity properties. An application to the reaction-diffusion problems with nonmonotone multivalued semilin…