Non-autonomous stochastic evolution equations in Banach spaces of martingale type 2: Strict solutions and maximal regularity

Tôn Việt Tạ

doi:10.3934/dcds.2017193

Article Contents

2017, Volume 37, Issue 8: 4507-4542. Doi: 10.3934/dcds.2017193

This issue Previous Article Existence, nonexistence and uniqueness of positive stationary solutions of a singular Gierer-Meinhardt system Next Article Measurable sensitivity via Furstenberg families

Non-autonomous stochastic evolution equations in Banach spaces of martingale type 2: Strict solutions and maximal regularity

Tôn Việt Tạ

Center for Promotion of International Education and Research, Faculty of Agriculture, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka 812-8581, Japan

Received: June 30, 2016

Revised: February 28, 2017

Published: May 2017

The author was supported by JSPS KAKENHI Grant Number 20140047.

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This paper is devoted to studying a non-autonomous stochastic linear evolution equation in Banach spaces of martingale type 2. We construct unique strict solutions to the equation and show their maximal regularity. The abstract results are then applied to stochastic diffusion equations.

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Mathematics Subject Classification: Primary: 60H15, 35R60; Secondary: 47D06.

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