Existence results for linear evolution equations of parabolic type

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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 languageEnglish
Pages (from-to)751-785
Number of pages35
JournalCommunications on Pure and Applied Analysis
Volume17
Issue number3
DOIs
Publication statusPublished - May 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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