Linear Sobolev Type Equations with Relatively p-Sectorial Operators in Space of ＂Noises

• Published in: Abstract and Applied Analysis Vol. 2015; no. 2015; pp. 128 - 135
• Main Authors: Favini, Angelo, Manakova, N. A., Sviridyuk, G. A.
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Limiteds 2015; Hindawi Publishing Corporation; John Wiley & Sons, Inc; Hindawi Limited
• Subjects: Boundary conditions; Derivatives; Initial conditions; Mathematical analysis; Mathematical research; Noise; Operator theory; Operators; Ordinary differential equations; Random variables; Stochastic analysis; Stochasticity; Studies; Uniqueness
• ISSN: 1085-3375; 1687-0409
• DOI: 10.1155/2015/697410

The concept of “white noise,” initially established in finite-dimensional spaces, is transferred to infinite-dimensional case. The goal of this transition is to develop the theory of stochastic Sobolev type equations and to elaborate applications of practical interest. To reach this goal the Nelson-Gliklikh derivative is introduced and the spaces of “noises” are developed. The Sobolev type equations with relatively sectorial operators are considered in the spaces of differentiable “noises.” The existence and uniqueness of classical solutions are proved. The stochastic Dzektser equation in a bounded domain with homogeneous boundary condition and the weakened Showalter-Sidorov initial condition is considered as an application.