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

abstract

• 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.

authors

• Titi, Edriss

published proceedings

• JOURNAL OF DIFFERENTIAL EQUATIONS

author list (cited authors)

• Katriel, G., Kupferman, R., & Titi, E. S.

citation count

• 0

complete list of authors

• Katriel, Guy||Kupferman, Raz||Titi, Edriss S

publication date

• November 2008

publisher

• Elsevier  Publisher

published in

• Journal of Differential Equations  Journal

keywords

• Equilibrium Manifold
• Global Attractor
• Quadratic Differential Systems
• Viscoelastic Toy Model

Digital Object Identifier (DOI)

• 10.1016/j.jde.2007.11.014

start page

• 2771

end page

• 2784

volume

• 245

issue

• 10

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2Fj.jde.2007.11.014