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

A variational principle for nonlinear transport equations

Nassif Ghoussoub 1,

1. 

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

Received  January 2005 Revised  June 2005 Published  September 2005

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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