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The weighted Inertia-Energy-Dissipation principle

delete2025-02-18
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Ulisse Stefanelli *
DOI：10.1142/S0218202525400019delete
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Abstract

Abstract

En 中文
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:
Variational principle
evolution equations
elliptic regularization
Euler-Lagrange equation
gradient flows
doubly nonlinear flows
rate-independent flows
semilinear waves

Journal

Mathematical Models and Methods in Applied Sciences cover
Mathematical Models and Methods in Applied Sciences
IF:
3
Papers:
2.2K
Citations:
4.6K

Organization

U
University of Vienna
Scholars:
1.7W
Papers: 1.6W
Citations: 40
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