Linear Sobolev Type Equations with Relatively p-Radial Operators in Space of “Noises”

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• 作者：Angelo Favini ; Georgy Sviridyuk ; Minzilia Sagadeeva
• 关键词：Stochastic Sobolev type equations ; “White noise”Space of “noises”Wiener process ; Additive “white noise”
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：13
• 期：6
• 页码：4607-4621
• 全文大小：584 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

Sobolev type equations now constitute a vast area of non-classical equations of mathematical physics. They include equations of mathematical physics, whose representation in the form of equations or systems of partial differential equations does not fit any of the classical types (elliptic, parabolic or hyperbolic). By the properties of the operators involved, the considered Sobolev type equation has a degenerate solving semigroup of class C₀ in suitable Banach spaces. We consider a Sobolev type stochastic equation in the spaces of random processes. The concepts previously introduced for the spaces of differentiable “noises” using the Nelson–Gliklikh derivative are carried over to the case of complex-valued “noises”. We construct a solution to the weakened Showalter–Sidorov problem for Sobolev type equation with relatively p-radial operator in a space of complex-valued processes.