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Nonsmooth analysis of doubly nonlinear evolution equations

Name: Nonsmooth analysis of doubly nonlinear evolution equations
Keywords: ddc:510, Doubly nonlinear equations -- differential inclusions -- generalized gradient flows -- finite-strain elasticity, finite-strain elasticity, article, 49Q20, 58E99, 35K85, 35K50, 510, 35A15

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type , Preprint , Report 03 Jan 2012Embargo end date: 01 Jan 2011 Italy, Germany Publisher:Springer Science and Business Media LLCJournal:Calculus of Variations and Partial Differential Equations, volume 46, pages 253-310 (issn: 0944-2669, eissn: 1432-0835,

Authors: Mielke Alexander; ROSSI, Riccarda; Savare' Giuseppe;

doi: 10.1007/s00526-011-0482-z , 10.48550/arxiv.1105.4296 , 10.20347/wias.preprint.1613

arXiv: http://arxiv.org/abs/1105.4296

handle: 11379/90511 , 11571/273711

Nonsmooth analysis of doubly nonlinear evolution equations

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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.

45 pages

Countries

Italy, Germany

Related Organizations

Humboldt-Universität zu Berlin
Germany
Leibniz Association
Germany
University of Pavia
Italy
Weierstrass Institute
Germany
Weierstrass Institute for Applied Analysis and Stochastics
Germany

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Keywords

ddc:510, Doubly nonlinear equations -- differential inclusions -- generalized gradient flows -- finite-strain elasticity, finite-strain elasticity, article, 49Q20, 58E99, 35K85, 35K50, 510, 35A15, generalized gradient flow, Mathematics - Analysis of PDEs, generalized gradient flows, differential inclusions, FOS: Mathematics, differential inclusion, Doubly nonlinear equation, Doubly nonlinear equations, Analysis of PDEs (math.AP)

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