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

Article type: Research Article

Authors: Poliakovsky, Arkady

Affiliations: Department of Mathematics, Ben Gurion University of the Negev, POB 653, Be'er Sheva 84105, Israel. E-mail: [email protected]

Abstract: 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.

Keywords: evolution equations, variational principles

DOI: 10.3233/ASY-131171

Journal: Asymptotic Analysis, vol. 85, no. 1-2, pp. 29-74, 2013