An existence result and evolutionary Gamma-convergence for perturbed gradient systems
- Bacho, Aras
- Emmrich, Etienne
- Mielke, Alexander
2010 Mathematics Subject Classification
- 35A15 35K50 35K85 49Q20 58E99
- Doubly nonlinear equations, differential inclusions, generalized gradient flows, perturbed gradient flows, evolutionary Gamma convergence, homogenization, reaction-diffusion systems
We consider the initial-value problem for the perturbed gradient flows, where a differential inclusion is formulated in terms of a subdifferential of an energy functional, a subdifferential of a dissipation potential and a more general perturbation, which is assumed to be continuous and to satisfy a suitable growth condition. Under additional assumptions on the dissipation potential and the energy functional, existence of strong solutions is shown by proving convergence of a semi-implicit discretization scheme with a variational approximation technique.
- J. Evol. Equ., 19 (2019), pp. 479--522, DOI 10.1007/s00028-019-00484-x .