Doubly nonlinear stochastic evolution equations
| Autor: | Ulisse Stefanelli, Luca Scarpa |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
Applied Mathematics Probability (math.PR) 010102 general mathematics existence Maximal monotone operators doubly nonlinear stochastic equations strong and martingale solutions generalized Ito's formula Stochastic evolution 01 natural sciences 010101 applied mathematics Stochastic partial differential equation Nonlinear system Mathematics - Analysis of PDEs generalized Itô's formula Modeling and Simulation FOS: Mathematics 35K55 35R60 60H15 Applied mathematics Nonlinear diffusion 0101 mathematics Mathematics - Probability Analysis of PDEs (math.AP) |
| Zdroj: | Mathematical models and methods in applied sciences 30 (2020): 991–1031. doi:10.1142/S0218202520500219 info:cnr-pdr/source/autori:L. Scarpa and U. Stefanelli/titolo:Doubly nonlinear stochastic evolution equations/doi:10.1142%2FS0218202520500219/rivista:Mathematical models and methods in applied sciences/anno:2020/pagina_da:991/pagina_a:1031/intervallo_pagine:991–1031/volume:30 |
| ISSN: | 1793-6314 0218-2025 |
| DOI: | 10.1142/s0218202520500219 |
| Popis: | We present an existence theory for martingale and strong solutions to doubly nonlinear evolution equations in a separable Hilbert space in the form $$d(Au) + Bu\,dt \ni F(u)\,dt + G(u)\,dW$$ where both $A$ and $B$ are maximal monotone operators, possibly multivalued, $F$ and $G$ are Lipschitz-continuous, and $W$ is a cylindrical Wiener process. Via regularization and passage-to-the-limit we show the existence of martingale solutions. The identification of the limit is obtained by a lower-semicontinuity argument based on a suitably generalized It\^o's formula. If either $A$ or $B$ is linear and symmetric, existence and uniqueness of strong solutions follows. Eventually, several applications are discussed, including doubly nonlinear stochastic Stefan-type problems. Comment: 34 pages |
| Databáze: | OpenAIRE |
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