Existence results for linear evolution equations of parabolic type

Tôn Viêt Ta

doi:10.3934/cpaa.2018039

Existence results for linear evolution equations of parabolic type

Tôn Viêt Ta

Attached Promotive Center for International Education and Research of Agriculture

Research output: Contribution to journal › Article › peer-review

Abstract

We study a stochastic parabolic evolution equation of the form dX + AXdt = F(t)dt + G(t)dW(t) in Banach spaces. Existence of mild and strict solutions and their space-time regularity are shown in both the deterministic and stochastic cases. Abstract results are applied to a nonlinear stochastic heat equation.

Original language	English
Pages (from-to)	751-785
Number of pages	35
Journal	Communications on Pure and Applied Analysis
Volume	17
Issue number	3
DOIs	https://doi.org/10.3934/cpaa.2018039
Publication status	Published - May 2018

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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title = "Existence results for linear evolution equations of parabolic type",

abstract = "We study a stochastic parabolic evolution equation of the form dX + AXdt = F(t)dt + G(t)dW(t) in Banach spaces. Existence of mild and strict solutions and their space-time regularity are shown in both the deterministic and stochastic cases. Abstract results are applied to a nonlinear stochastic heat equation.",

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AB - We study a stochastic parabolic evolution equation of the form dX + AXdt = F(t)dt + G(t)dW(t) in Banach spaces. Existence of mild and strict solutions and their space-time regularity are shown in both the deterministic and stochastic cases. Abstract results are applied to a nonlinear stochastic heat equation.

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