Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids

Details Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids

2007-10-12

arxiv.org/abs/0710.2384v1

Mathematics

Dynamical Systems

Scientific paper

We study a class of quadratic, infinite-dimensional dynamical systems, inspired by models for viscoelastic fluids. We prove that these equations define a semi-flow on the cone of positive, essentially bounded functions. As time tends to infinity, the solutions tend to an equilibrium manifold in the $L^2$-norm. Convergence to a particular function on the equilibrium manifold is only proved under additional assumptions. We discuss several possible generalizations.

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