Variational resolution for some general classes of nonlinear evolutions. Part I

Arkady Poliakovsky

Published 2011-12-10, updated 2013-08-08Version 12

We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the minimizer of the appropriate energy functional but also any critical point must be a solution of the corresponding evolutional system.