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

研究成果: Article査読

18 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)32-56
ページ数25
ジャーナルJournal of Differential Equations
231
1
DOI
出版ステータスPublished - 2006 12 1
外部発表はい

ASJC Scopus subject areas

  • 分析
  • 応用数学

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