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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.

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Authors and Affiliations

  1. Weierstraß-Institut, Mohrenstraße 39, 10117, Berlin, Germany

    Alexander Mielke

  2. Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489, Berlin (Adlershof), Germany

    Alexander Mielke

  3. Dipartimento di Matematica, Università di Brescia, via Valotti 9, 25133, Brescia, Italy

    Riccarda Rossi

  4. Dipartimento di Matematica “F. Casorati”, Università di Pavia, Via Ferrata, 1, 27100, Pavia, Italy

    Giuseppe Savaré

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  1. Alexander Mielke
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  2. Riccarda Rossi
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  3. Giuseppe Savaré
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Correspondence to Giuseppe Savaré.

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Communicated by J. Ball.

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Mielke, A., Rossi, R. & Savaré, G. Nonsmooth analysis of doubly nonlinear evolution equations. Calc. Var. 46, 253–310 (2013). https://doi.org/10.1007/s00526-011-0482-z

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