38 citations · 182 across the 59 of their papers we have counts for
5 papers · 2 filters
Global attractor and stabilization for a coupled PDE-ODE system
Messoud Efendiev, Sergey Zelik
We study the asymptotic behavior of solutions of one coupled PDE-ODE system arising in mathematical biology as a model for the development of a forest ecosystem. In the case where…
Attractors for the nonlinear elliptic boundary value problems and their parabolic singular limit
Mark I. Vishik, Sergey V. Zelik
We apply the dynamical approach to the study of the second order semi-linear elliptic boundary value problem in a cylindrical domain with a small parameter at the second derivative…
Asymptotic uniform boundedness of energy solutions to the Penrose-Fife model
Giulio Schimperna, Antonio Segatti, Sergey Zelik
We study a Penrose-Fife phase transition model coupled with homogeneous Neumann boundary conditions. Improving previous results, we show that the initial value problem for this mod…
Counterexamples to the regularity of Mane projections and global attractors
Alp Eden, Varga Kalanarov, Sergey Zelik
We study the global attractors of abstract semilinear parabolic equations and their projections to finite-dimensional planes. It is well-known that the attractor can be embedded in…
Smooth Attractors for the Brinkman-Forchheimer equations with fast growing nonlinearities
Varga K. Kalantarov, Sergey Zelik
We prove the existence of regular dissipative solutions and global attractors for the 3D Brinkmann-Forchheimer equations with the nonlinearity of an arbitrary polynomial growth rat…