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

TL;DR

This paper introduces a variational method for solving broad classes of nonlinear evolution equations, deriving solutions directly from Euler-Lagrange equations, and establishing that critical points correspond to solutions.

Contribution

It presents a novel variational approach that links critical points of energy functionals to solutions of nonlinear evolution systems, expanding the theoretical framework.

Findings

Critical points of the energy functional are solutions.

The method applies to wide classes of nonlinear evolutions.

Solutions can be obtained directly from Euler-Lagrange equations.

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.