Evolution inclusions governed by subdifferentials in reflexive Banach spaces. (English) Zbl 1081.34059

Akagi, Goro; Ôtani, Mitsuharu

J. Evol. Equ. 4, No. 4, 519-541 (2004).

Let \(V\) be a real reflexive Banach space; \(V^*\) its dual space; \(\varphi : V \rightarrow (-\infty, +\infty]\) a lower semicontinuous functional and \(\partial \varphi\) its subdifferential. Using the nonlinear semigroup approach, the authors study the existence, uniqueness and regularity of strong solutions of the Cauchy problem and the periodic problem for the evolution inclusion in \(V^*\) \[ du(t)/dt + \partial \varphi (u(t)) \ni f(t), \quad t \in (0,T). \] Some applications to the nonlinear heat equations governed by \(p\)–Laplace operators in bounded and unbounded domains are given.

Reviewer: Valerii V. Obukhovskij (Voronezh)

MSC:

34G25	Evolution inclusions
34C25	Periodic solutions to ordinary differential equations
35K55	Nonlinear parabolic equations
35K65	Degenerate parabolic equations

Keywords:

evolution inclusion; strong solution; periodic solution; existence; uniqueness; regularity; heat equation; subdifferential