Zehra Şen | Searcharxiv

arXiv2026

Attractors for Singular-Degenerate Porous Medium Type Equations Arising in Models for Biofilm Growth

We investigate the long-time behaviour of solutions of a class of singular-degenerate porous medium type equations in bounded domains with homogeneous Dirichlet boundary conditions. The existence of global attractors is shown under very general assumptions. Assuming, in addition, that solutions are globally Hölder continuous and the reaction terms satisfy a suitable sign condition in the vicinity of the degeneracy, we also prove the existence of an exponential attractor, which, in turn, yields the finite fractal dimension of the global attractor. Moreover, we extend the results for scalar equations to systems where the degenerate equation is coupled to a semilinear reaction-diffusion equation. The study of such systems is motivated by models for biofilm growth.

math.AP↗

arXiv2016

Attractors for the strongly damped wave equation with $p$-Laplacian

This paper is concerned with the initial boundary value problem for one dimensional strongly damped wave equation involving $p$-Laplacian. For $p>2$, we establish the existence of weak local attractors for this problem in $W_{0}^{1,p}(0,1)\times L^{2}(0,1)$. Under restriction $2<p<4$, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in $W_{0}^{1,p}(0,1)\times L^{2}(0,1)$ and this attractor is a bounded subset of $W^{1,\infty }(0,1)\times W^{1,\infty }(0,1)$.

math.AP↗