Evolution inclusions governed by subdifferentials in reflexive Banach spaces

Goro Akagi, Mitsuharu Otani

    Research output: Contribution to journalArticle

    19 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)519-541
    Number of pages23
    JournalJournal of Evolution Equations
    Volume4
    Issue number4
    DOIs
    Publication statusPublished - 2004 Dec

    Keywords

    • Evolution equation
    • Reflexive Banach space
    • Subdifferential

    ASJC Scopus subject areas

    • Ecology, Evolution, Behavior and Systematics

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