Martedì, 10 Novembre 2015, ore 15 (precise), Dr. Matteo Muratori, University of Pavia, presso la sala conferenze dell'IMATI-CNR di Pavia, terrà un seminario dal titolo: 

EXISTENCE AND UNIQUENESS RESULTS FOR THE POROUS MEDIUM EQUATION WITH MEASURE DATA ON CARTAN-HADAMARD MANIFOLDS

nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e Dipartimento di Matematica, Pavia).
Al termine della conferenza sarà organizzato un piccolo rinfresco.

 

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Abstract

This talk deals with the Cauchy problem for the porous medium equation on complete, simply connected Riemannian manifolds M having nonpositive sectional curvatures, namely Cartan-Hadamard manifolds. In addition, we also require that the Ricci curvature is bounded from below by a negative constant times the square of the geodesic distance from a pole. We show existence of weak solutions whose initial datum is a finite Radon measure on M, not necessarily positive. Moreover, such solutions satisfy a suitable smoothing effect (in fact they are bounded for positive times) and conserve the mass. As for uniqueness, we first establish some results in potential analysis on nonparabolic manifolds, which concern the validity of a modified version of the mean-value inequality for superharmonic functions and properties of potentials of positive Radon measures. These tools turn out to be crucial in order to prove uniqueness in the class of nonnegative weak solutions.

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Pagina web del Seminario di Matematica Applicata:
http://matematica.unipv.it/it/seminari-matematica-applicata

Vecchia pagina web con archivio dei vecchi seminari:
http://www-dimat.unipv.it/~seminari/matematica-applicata.html