The Weighted Inertia-Energy-Dissipation Principle
Analysis of PDEs
2024-07-31 v1
Abstract
The Weighted Inertia-Energy-Dissipation (WIDE) principle is a global variational approach to nonlinear evolution equations of parabolic and hyperbolic type. The minimization of the parameter-dependent WIDE functional on trajectories delivers an elliptic-in-time regularization. By taking the limit in the parameter, one recovers a solution to the given differential problem. This survey is intended to provide a comprehensive account of the available results on the WIDE variational approach. The basic concepts are illustrated in the simplest finite-dimensional case, and the existing literature, both theoretical and applied, is systematically reviewed.
Keywords
Cite
@article{arxiv.2407.20933,
title = {The Weighted Inertia-Energy-Dissipation Principle},
author = {Ulisse Stefanelli},
journal= {arXiv preprint arXiv:2407.20933},
year = {2024}
}