Gradient flows of non convex functionals in Hilbert spaces and
 applications

Riccarda Rossi; Giuseppe Savaré

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Displaying similar documents to “Gradient flows of non convex functionals in Hilbert spaces and applications”

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 $H$ $\{\begin{matrix} u^{'} (t) + \partial φ (u (t)) ∋ 0 a.e. in (0, T), \\ u (0) = u_{0}, \end{matrix}$ where $φ : H \to (- \infty, + \infty]$ is a proper, lower semicontinuous functional which is not supposed to be a (smooth perturbation of a) convex functional and $\partial φ$ 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...

A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems

Michael Ortiz, Alexander Mielke (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems...