Finite dimensional attractors for binary mixtures of viscoelastic bodies

Abstract

We consider a class of semilinear problems for binary mixtures in the presence of viscoelastic dissipation. This paper aims to study the existence and properties of long-time dynamics in a two-dimensional setting. More precisely, we first prove the existence of a finite-dimensional global attractor that exhibits additional regularity in higher topology. Secondly, we show that the dynamical system has a generalized fractal exponential attractor.

COMMUNICATED BY:

• Irena Lasiecka

Keywords:

• Mixtures problems
• global attractor
• fractal dimension
• exponential attractor

Subject classifications:

• 35B41
• 35L53
• 74K10

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001, and by Fundação de Amparo à Pesquisa do Estado de Minas Gerais (FAPEMIG).