A variational principle for nonlinear transport equations
Nassif Ghoussoub - Department of Mathematics, The University of British Columbia, Vancouver BC Canada V6T 1Z2, Canada (email)
Abstract: We verify -after appropriate modifications- an old conjecture of Brezis-Ekeland  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  and other parabolic evolution equations ().
Keywords: Transport equation, convex duality
Received: January 2005; Revised: June 2005; Published: September 2005.
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