Attractors for Singular-Degenerate Porous Medium Type Equations Arising in Models for Biofilm Growth
Applied Mathematics and Optimization, vol.94, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 94 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1007/s00245-026-10458-4
- Journal Name: Applied Mathematics and Optimization
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, ABI/INFORM, Aerospace Database, Compendex, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Business Source Ultimate (EBSCO), Engineering Source (EBSCO), Materials Science & Engineering Collection (ProQuest), Pharma Collection (ProQuest), Technology Collection (ProQuest)
- Keywords: Attractor, Biofilm, Fractal dimension, Mixed boundary condition, Quasilinear degenerate reaction diffusion system, Slow/fast diffusion
- Open Archive Collection: AVESIS Open Access Collection
- Hacettepe University Affiliated: Yes
Abstract
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.