Evolution inclusions governed by subdifferentials in reflexive Banach spaces

Goro Akagi, Mitsuharu Otani

    研究成果: Article

    15 引用 (Scopus)

    抄録

    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.

    元の言語English
    ページ(範囲)519-541
    ページ数23
    ジャーナルJournal of Evolution Equations
    4
    発行部数4
    DOI
    出版物ステータスPublished - 2004 12

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    Evolution Inclusion
    Reflexive Banach Space
    Subdifferential
    Hilbert space
    Subdifferential Operator
    Periodic Problem
    Strong Solution
    Evolution Equation
    Cauchy Problem
    Existence and Uniqueness
    Regularity
    methodology
    Banach space
    Approximation

    ASJC Scopus subject areas

    • Ecology, Evolution, Behavior and Systematics

    これを引用

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