We present an existence result for a partial differential inclusion with linear parabolic principal part and relaxed one-sided Lipschitz multivalued nonlinearity in the framework of Gelfand triples. Our study uses discretizations of the differential inclusion by a Galerkin scheme, which is compatible with a conforming finite element method, and we analyze convergence properties of the discrete solution sets.
- Analysis of partial differential inclusions
- Convergence of solution sets
- Galerkin method
- Relaxed one-sided Lipschitz condition
- Semilinear parabolic inclusion