Transport Equations with Fractal Noise - Existence, Uniqueness and Regularity of the Solution

被引:8
作者
Issoglio, Elena [1 ]
机构
[1] Kings Coll London, Dept Math, London WC2R 2LS, England
来源
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 2013年 / 32卷 / 01期
关键词
Transport equation; non-smooth coefficients; fractional Brownian noise; stochastic partial differential equation; EVOLUTION-EQUATIONS;
D O I
10.4171/ZAA/1473
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems on bounded smooth domains with Dirichlet boundary conditions by means of semigroup theory and fixed point arguments. Main ingredients are the definition of a product of a function and a (not too irregular) distribution as well as a corresponding norm estimate As an application, transport stochastic partial differential equations driven by fractional Brownian noises are considered in the pathwise sense.
引用
收藏
页码:37 / 53
页数:17
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