Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces

Research output: Contribution to journalArticlepeer-review

18 Citations (Scopus)

Abstract

We prove the existence of solutions of the Cauchy problem for the doubly nonlinear evolution equation: d v (t) / d t + ∂V φt (u (t)) ∋ f (t), v (t) ∈ ∂H ψ (u (t)), 0 < t < T, where ∂H ψ (respectively, ∂V φt) denotes the subdifferential operator of a proper lower semicontinuous functional ψ (respectively, φt explicitly depending on t) from a Hilbert space H (respectively, reflexive Banach space V) into (- ∞, + ∞] and f is given. To do so, we suppose that V {right arrow, hooked} H ≡ H* {right arrow, hooked} V* compactly and densely, and we also assume smoothness in t, boundedness and coercivity of φt in an appropriate sense, but use neither strong monotonicity nor boundedness of ∂H ψ. The method of our proof relies on approximation problems in H and a couple of energy inequalities. We also treat the initial-boundary value problem of a non-autonomous degenerate elliptic-parabolic problem.

Original languageEnglish
Pages (from-to)32-56
Number of pages25
JournalJournal of Differential Equations
Volume231
Issue number1
DOIs
Publication statusPublished - 2006 Dec 1
Externally publishedYes

Keywords

  • Doubly nonlinear evolution equation
  • Elliptic-parabolic problem
  • Reflexive Banach space
  • Subdifferential

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'Doubly nonlinear evolution equations governed by time-dependent subdifferentials in reflexive Banach spaces'. Together they form a unique fingerprint.

Cite this