Searcharxiv⌕ Search

arXiv subjects

Oleksiy V. Kapustyan

Publications and source records attributed to Oleksiy V. Kapustyan.

4 recordsLinked to original sources
arXiv2025

Chain recurrence and structure of omega-limit sets of multivalued semiflows

We study properties of !-limit sets of multivalued semiflows like chain recurrence or the existence of cyclic chains. First, we prove that under certain conditions the omega-limit set of a trajectory is chain recurrent, applying this result to an evolution differential inclusion with upper semicontinous right-hand side. Second, we give conditions ensuring that the omega-limit set of a trajectory contains a cyclic chain. Using this result we are able to check that the omega-limit set of every trajectory of a reaction-diffusion equation without uniqueness of solutions is an equilibrium.

math.DS↗
arXiv2020

Asymptotic gain results for attractors of semilinear systems

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee--Infante equations, for example.

math.AP↗
arXiv2012

Structure and regularity of the global attractor of a reaction-di§usion equation with non-smooth nonlinear term

In this paper we study the structure of the global attractor for a reaction- di§usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable manifold of the set of stationary points or the stable one but considering in this last case only solutions in the set of bounded complete trajectories.

math.DS↗