Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Attractors for Singular-Degenerate Porous Medium Type Equations Arising in Models for Biofilm Growth (2502.16649v1)

Published 23 Feb 2025 in math.AP and math.DS

Abstract: We investigate the long-time behaviour of solutions of a class of singular-degenerate porous medium type equations in bounded Lipschitz domains with mixed Dirichlet-Neumann boundary conditions. The existence of global attractors is shown under very general assumptions. Assuming, in addition, that solutions are globally H\"older 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.

Summary

We haven't generated a summary for this paper yet.