A variational principle for nonlinear transport equations | Zendy

Nassif Ghoussoub | Zendy

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A variational principle for nonlinear transport equations

Author(s) -

Nassif Ghoussoub

Publication year - 2005

Publication title -

communications on pure andamp applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.077

H-Index - 42

eISSN - 1553-5258

pISSN - 1534-0392

DOI - 10.3934/cpaa.2005.4.735

Subject(s) - uniqueness , variational principle , mathematics , nonlinear system , euler equations , calculus of variations , mathematical analysis , duality (order theory) , conjecture , euler–lagrange equation , regular polygon , physics , pure mathematics , lagrangian , geometry , quantum mechanics

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]).

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