Tuesday, 10 November 2015, 3 p.m. (sharp), Dr. Matteo Muratori, University of Pavia, at the conference room of IMATI-CNR in Pavia, will give a lecture titled:

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

as part of the Applied Mathematics Seminar (IMATI-CNR e Dipartimento di Matematica, Pavia).
At the end a refreshment will be organized. 

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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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web page of the Applied Mathematics Seminar:
http://matematica.unipv.it/it/seminari-matematica-applicata

old web page of the Applied Mathematics Seminar:
http://www-dimat.unipv.it/~seminari/matematica-applicata.html