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Seventh Mississippi State - UAB Conference on Differential Equations & Computational Simulations
November 1-3, 2007
Doubletree Hotel
Birmingham, AL, USA

Organizers
Mississippi State University & University of Alabama - Birmingham

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Existence and Regularity of Solutions to Doubly Nonlinear Diffusion Equations
by
Jochen Merker
University of Rostock

Under weak assumptions on p, m and f we prove existence and regularity of weak solutions to doubly nonlinear diffusion equations du/dt=div( (∇um)p-1 ) + f(u) by optimal a priori estimates for ∥u(t)∥r(t) with a time-dependent exponent r(t). These a priori estimates are obtained in an elementary way by logarithmic Gagliardo-Nirenberg inequalities and guarantee not only ultracontractivity of the generated nonlinear semigroup, but also the existence of a global attractor.

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Date received: September 17, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavp-14.