A variational principle for nonlinear transport equations

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December 2005, 4(4): 735-742. doi: 10.3934/cpaa.2005.4.735

A variational principle for nonlinear transport equations

1.	Department of Mathematics, The University of British Columbia, Vancouver BC Canada V6T 1Z2

Received January 2005 Revised June 2005 Published September 2005

Abstract
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We verify -after appropriate modifications- an old conjecture of Brezis-Ekeland [4] concerning the feasibility of a global and variational approach to the problems of existence and uniqueness of solutions of non-linear transport equations, which do not normally fit in an Euler-Lagrange framework. Our method is based on a concept of "anti-self duality" that seems to be inherent in many problems, including gradient flows of convex energy functionals treated in [10] and other parabolic evolution equations ([7]).

Keywords: Transport equation, convex duality.

Mathematics Subject Classification: 35F30, 35A15.

Citation: Nassif Ghoussoub. A variational principle for nonlinear transport equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 735-742. doi: 10.3934/cpaa.2005.4.735

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