Calculus of Variations and Geometric Measure Theory

A. Mielke - R. Rossi - G. Savaré

Nonsmooth analysis of doubly nonlinear evolution equations

created by rossi on 21 May 2011
modified on 11 Jul 2012


Submitted Paper

Inserted: 21 may 2011
Last Updated: 11 jul 2012

Pages: 45
Year: 2011


In this paper we analyze a broad class of abstract doubly nonlinear evolution equations in Banach spaces, driven by nonsmooth and nonconvex energies. We provide some general sufficient conditions, on the dissipation potential and the energy functional, for existence of solutions to the related Cauchy problem. We prove our main existence result by passing to the limit in a time-discretization scheme with variational techniques. Finally, we discuss an application to a material model in finite-strain elasticity.

Keywords: doubly nonlinear equations , differential inclusions, generalized gradient flows, finite-strain elasticity