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arXiv · 1105.4296

Nonsmooth analysis of doubly nonlinear evolution equations

Alexander Mielke·Riccarda Rossi·Giuseppe Savare'
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Abstract

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.

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Alexander Mielke, Riccarda Rossi, Giuseppe Savare'. 2011-05-21. Nonsmooth analysis of doubly nonlinear evolution equations. https://doi.org/10.1007/s00526-011-0482-z

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