The Energy-Dissipation Principle for stochastic parabolic equations

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.

arXiv comment23 pages

References in corpus (5)

• Stability of solutions to stochastic partial differential equations
• A variational approach to dissipative SPDEs with singular drift
• Exploring families of energy-dissipation landscapes via tilting -- three types of EDP convergence
• Well-posedness for a class of doubly nonlinear stochastic PDEs of divergence type
• Penalization via global functionals of optimal-control problems for dissipative evolution