Displaying similar documents to “A generalization of Aubry-Mather theory to partial differential equations and pseudo-differential equations”

Existence and approximation results for gradient flows

Riccarda Rossi, Giuseppe Savaré (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space H u ' ( t ) + ∂ φ ( u ( t ) ) ∋ 0 a.e. in ( 0 , T ) , u ( 0 ) = u 0 , where φ : H → ( - ∞ , + ∞ ] is a proper, lower semicontinuous functional which is not supposed to be a (smooth perturbation of a) convex functional and ∂ φ is (a suitable limiting version of) its subdifferential. The interest for this kind of equations is motivated by a number of examples, which show that several mathematical models describing phase transitions phenomena and leading to systems of evolutionary...