Nonsmooth analysis of doubly nonlinear evolution equations

By Alexander Mielke, Riccarda Rossi, Giuseppe Savar'e. 2011

112 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/ebd1659bd3c5818f446d89a2a3b14aac907359b3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Alexander Mielke
2. Giuseppe Savar'e
3. Riccarda Rossi
4. Nguyen D. Hoang
5. Giovanni Colombo
6. Boris S. Mordukhovich
7. René Henrion
8. Matthias Erbar

In Computational Theory and Mathematics

1. Alexander Mielke
2. Giuseppe Savar'e
3. Riccarda Rossi
4. Boris S. Mordukhovich
5. René Henrion
6. Nguyen D. Hoang
7. Giovanni Colombo
8. Alexander Y. Kruger

In Materials Chemistry

1. Giuseppe Savar'e
2. Riccarda Rossi
3. Alexander Mielke

Citations in the corpus

• BV SOLUTIONS AND VISCOSITY APPROXIMATIONS OF RATE-INDEPENDENT SYSTEMS ∗ (2009, background): “Then (6.20) follows by the identity m(s) = Rγ(x(s); ẋ(s)).”
• Optimal control of the sweeping process over polyhedral controlled sets (2015, background): “Let us also mention the recent paper [21], which contains existence and well-posedness results obtained via advanced tools of variational analysis and generalized differentiation for a broad class of evolution systems including the sweeping process.”
• Gradient flows and Evolution Variational Inequalities in metric spaces. I: Structural properties (2018, unknown): “[80, 68]) and a broadening of the structure of the ambient space, from Hilbert to Banach spaces (for the theory of doubly nonlinear evolution equations, see e.”