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In this paper we analyze a broad class of abstract doubly nonlinear evolution equa- tions 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.

Nonsmooth analysis of doubly nonlinear evolution equations

SAVARE', GIUSEPPE
2013-01-01

Abstract

In this paper we analyze a broad class of abstract doubly nonlinear evolution equa- tions 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.
2013
The Mathematics category includes resources dealing with mathematics, applied mathematics, statistics and probability.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
sì
WOS:000313161600012
2-s2.0-84871941128
Esperti anonimi
Inglese
Internazionale
STAMPA
46
253
310
58
Attracts and collects many of the important top-quality contributions to this field of research. Stresses the interactions between analysts, geometers, and physicists. A section called "News and Views" offers an opportunity for communication among scientists working in the field by featuring discussions, announcements of meetings, reproductions of historical documents, and bibliographies. Calculus of Variations and Partial Differential Equations attracts and collects many of the important top-quality contributions to this field of research, and stresses the interactions between analysts, geometers, and physicists. In addition, it offers an opportunity for communication among scientists working in the field through a section called "News and Views," which is open to discussions, announcements of meetings, reproductions of historical documents, and bibliographies. Coverage in the journal includes: - Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory - Variational methods for partial differential equations, linear and nonlinear eigenvalue problems, bifurcation theory - Variational problems in differential and complex geometry - Variational methods in global analysis and topology - Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems - Variational methods in mathematical physics, nonlinear elasticity, crystals, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions - Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.
Doubly nonlinear equations; differential inclusions; generalized gradient flows; finite-strain elasticity
http://arxiv.org/abs/1105.4296
3
info:eu-repo/semantics/article
262
Alexander, Mielke; Riccarda, Rossi; Savare', Giuseppe
1 Contributo su Rivista::1.1 Articolo in rivista
none
1.1 Articolo in rivista
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/273711
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