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A metric approach to a class of doubly nonlinear evolution equations and applications

Riccarda Rossi, Alexander Mielke, Giuseppe Savaré (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

This paper deals with the analysis of a class of doubly nonlinear evolution equations in the framework of a general metric space. We propose for such equations a suitable metric formulation (which in fact extends the notion of Curve of Maximal Slopefor gradient flows in metric spaces, see [5]), and prove the existence of solutions for the related Cauchy problem by means of an approximation scheme by time discretization. Then, we apply our results to obtain the existence of solutions to abstract...

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