Evolution inclusions governed by subdifferentials in reflexive Banach spaces

Goro Akagi, Mitsuharu Ôtani

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 1
Externally publishedYes

Keywords

  • Evolution equation
  • Reflexive Banach space
  • Subdifferential

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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