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

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