Convolution solutions of an abstract stochastic Cauchy problem

2010 ◽  
Vol 46 (6) ◽  
pp. 808-817
Author(s):  
S. V. Zdobnova
Keyword(s):  
Cauchy Problem ◽  
Stochastic Cauchy Problem

scholarly journals ON STOCHASTIC GENERALIZED FUNCTIONS

2011 ◽  
Vol 14 (02) ◽  
pp. 237-260 ◽  
Author(s):  
PEDRO CATUOGNO ◽  
CHRISTIAN OLIVERA
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Generalized Functions ◽  
Uniqueness Of The Solution ◽  
Stochastic Cauchy Problem

In this work we introduce a new algebra of stochastic generalized functions. The regular Hida distributions in [Formula: see text] are embedded in this algebra via their chaos expansions. As an application, we prove the existence and uniqueness of the solution of a stochastic Cauchy problem involving singularities.

scholarly journals Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Irina V. Melnikova ◽  
Uljana A. Alekseeva
Keyword(s):  
Cauchy Problem ◽  
White Noise ◽  
Quasilinear Equation ◽  
Abstract Cauchy Problem ◽  
Generalized Solutions ◽  
Nonlinear Perturbations ◽  
Colombeau Algebra ◽  
Integrated Semigroup ◽  
Noise Type ◽  
Stochastic Cauchy Problem

Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. An abstract stochastic Colombeau algebra is constructed, and solutions in the algebra are studied.

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