THE ENERGY-DISSIPATION PRINCIPLE FOR STOCHASTIC PARABOLIC EQUATIONS

Author(s)

Luca Scarpa, Ulisse Stefanelli

Abstract

The Energy-Dissipation Principle provides a variational tool for the analysis of parabolic evolution problems: solutions are characterized as so-called null-minimizers of a global functional on entire trajectories. This variational technique allows for applying the general results of the calculus of variations to the underlying differential problem and has been successfully applied in a variety of deterministic cases, ranging from doubly nonlinear flows to curves of maximal slope in metric spaces. The aim of this note is to extend the Energy-Dissipation Principle to stochastic parabolic evolution equations. Applications to stability and optimal control are also presented.

Organisation(s)

Department of Mathematics, Research Platform Accelerating Photoreaction Discovery

External organisation(s)

Politecnico di Milano, Institute of Genetics and Biophysics "Adriano Buzzati-Traverso", CNR

Journal

Advances in Mathematical Sciences and Applications

Volume

30

Pages

429-452

No. of pages

24

ISSN

1343-4373

Publication date

2021

Peer reviewed

Yes

Austrian Fields of Science 2012

101002 Analysis

Keywords

ASJC Scopus subject areas

Analysis, Applied Mathematics, Modelling and Simulation, Numerical Analysis

Portal url

https://ucrisportal.univie.ac.at/en/publications/the-energydissipation-principle-for-stochastic-parabolic-equations(d2197cfd-8865-461c-85ea-be01e3b6e7cc).html