WIAS Preprint No. 1613, (2011)

Nonsmooth analysis of doubly nonlinear evolution equations


  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888
  • Rossi, Riccarda
    ORCID: 0000-0002-7808-0261
  • Savaré, Giuseppe
    ORCID: 0000-0002-0104-4158

2010 Mathematics Subject Classification

  • 35A15 35K50 35K85 49Q20 58E99


  • Doubly nonlinear equations, differential inclusions, generalized gradient flows, finite-strain elasticity




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.

Appeared in

  • Calc. Var. Partial Differ. Equ., 46 (2013) pp. 253--310.

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