scholarly journals Stochastic Cauchy Problem in Hilbert Spaces: Models, Examples, Solutions

2016 ◽  
Vol 9 (4) ◽  
pp. 63-72
Author(s):  
O.S. Starkova ◽  
Keyword(s):  
Cauchy Problem ◽  
Hilbert Spaces ◽  
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 Sensitivity of a Fractional Integrodifferential Cauchy Problem of Volterra Type

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Dariusz Idczak ◽  
Andrzej Skowron ◽  
Stanisław Walczak
Keyword(s):  
Cauchy Problem ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Functional Parameter ◽  
Volterra Type ◽  
Main Assumption ◽  
Palais Smale Condition ◽  
Uniqueness Of A Solution

We prove a theorem on the existence and uniqueness of a solution as well as on a sensitivity (i.e., differentiable dependence of a solution on a functional parameter) of a fractional integrodifferential Cauchy problem of Volterra type. The proof of this result is based on a theorem on diffeomorphism between Banach and Hilbert spaces. The main assumption is the Palais-Smale condition.

scholarly journals On the Cauchy problem for semilinear elliptic equations

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
Nguyen Huy Tuan ◽  
Tran Thanh Binh ◽  
Tran Quoc Viet ◽  
Daniel Lesnic
Keyword(s):  
Cauchy Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Hilbert Spaces ◽  
Elliptic Equations ◽  
Elliptic Partial Differential Equations ◽  
Semilinear Elliptic Equations ◽  
Semilinear Elliptic ◽  
The Cauchy Problem ◽  
Ill Posed

AbstractWe study the Cauchy problem for nonlinear (semilinear) elliptic partial differential equations in Hilbert spaces. The problem is severely ill-posed in the sense of Hadamard. Under a weak

On mild solutions of gradient systems in Hilbert spaces

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Andrzej Rozkosz
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Mild Solutions ◽  
Backward Stochastic Differential Equations ◽  
Stochastic Representation ◽  
Infinite Dimensional ◽  
The Cauchy Problem

AbstractWe consider the Cauchy problem for an infinite-dimensional Ornstein-Uhlenbeck equation perturbed by gradient of a potential. We prove some results on existence and uniqueness of mild solutions of the problem. We also provide stochastic representation of mild solutions in terms of linear backward stochastic differential equations determined by the Ornstein-Uhlenbeck operator and the potential.

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