A variational principle for nonlinear transport equations

Pages: 735 - 742, Volume 4, Issue 4, December 2005

doi:10.3934/cpaa.2005.4.735       Abstract        Full Text (185.5K)       Related Articles

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 [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

Received: January 2005;      Revised: June 2005;      Published: September 2005.