1. Existence results for linear evolution equations of parabolic type
- Author
-
Tôn Việt Tạ
- Subjects
Physics ,Applied Mathematics ,Probability (math.PR) ,010102 general mathematics ,Mathematical analysis ,Banach space ,General Medicine ,Type (model theory) ,60H15, 35R60 ,01 natural sciences ,010101 applied mathematics ,Nonlinear system ,Evolution equation ,FOS: Mathematics ,Heat equation ,0101 mathematics ,Mathematics - Probability ,Analysis - Abstract
We study both strict and mild solutions to parabolic evolution equations of the form $dX+AXdt=F(t)dt+G(t)dW(t)$ in Banach spaces. First, we explore the deterministic case. The maximal regularity of solutions has been shown. Second, we investigate the stochastic case. We prove existence of strict solutions and show their space-time regularity. Finally, we apply our abstract results to a stochastic heat equation., Comment: 42 pages
- Published
- 2018
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