The existence, uniqueness and regularity of strong solutions for Cauchy problem and periodic problem are studied for the evolution equation: du(t)/dt + ∂φ(u(t)) ∋ f(t), t ∈]0, T[, where ∂φ is the so-called subdifferential operator from a real Banach space V into its dual V*. The study in the Hilbert space setting (V = V* = H: Hilbert space) is already developed in detail so far. However, the study here is done in the V-V* setting which is not yet fully pursued. Our method of proof relies on approximation arguments in a Hilbert space H. To assure this procedure, it is assumed that the embeddings V ⊂ H ⊂ V* are both dense and continuous.
- Evolution equation
- Reflexive Banach space
ASJC Scopus subject areas
- Ecology, Evolution, Behavior and Systematics