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arXiv · 2407.20933

The Weighted Inertia-Energy-Dissipation Principle

Ulisse Stefanelli
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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.

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Ulisse Stefanelli. 2024-07-30. The Weighted Inertia-Energy-Dissipation Principle. https://arxiv.org/abs/2407.20933

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