Long-time limit for a class of quadratic infinite-dimensional dynamical systems inspired by models of viscoelastic fluids
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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 L2-norm. Convergence to a particular function on the equilibrium manifold is only proved under additional assumptions. We discuss several possible generalizations. © 2008 Elsevier Inc. All rights reserved.
author list (cited authors)
Katriel, G., Kupferman, R., & Titi, E. S.