4 citations · 5 across the 5 of their papers we have counts for
10 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…