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The initial value problem for stochastic reaction-diffusion equations with continuous reaction

 

作者: Ralf Manthey,   Katrin Mittmann,  

 

期刊: Stochastic Analysis and Applications  （Taylor Available online 1997）
卷期: Volume 15, issue 4  

页码: 555-583

 

ISSN:0736-2994

 

年代: 1997

 

DOI:10.1080/07362999708809495

 

出版商: Marcel Dekker, Inc.

 

关键词: Stochastic Reaction-Diffusion Equation;Stochastic Integral;Generalized Random Field;Growth of Random Functions;Comparison theorem

 

数据来源: Taylor

 

摘要:

We give general conditions for existence and uniqueness of mild solutions to the initial value problem for stochastic reaction-diffusion equations with an additive (i.e. state-independent) noise which is coloured in space and white in time. The method represented here analogously works in the space-time white noise case. We essentially make use of a growth estimate for continuous random fields which helps to establish a Banach space in which the solution lives

 

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