Estimation and Control Problems for Stochastic Partial Differential Equations

2013 ◽  
Author(s):  
Pavel S. Knopov ◽  
Olena N. Deriyeva
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Control Problems ◽  
Partial Differential ◽  
Estimation And Control ◽  
And Control

Boundary and Interior Control for Partial Differential Equations

1975 ◽  
Vol 27 (1) ◽  
pp. 200-217 ◽  
Author(s):  
Robert Delver
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Control Problems ◽  
Partial Differential ◽  
And Control ◽  
Class Of Functions ◽  
Admissible Functions

From the time that the basic existence and regularity problems for partial differential equations have been solved many interesting new variational and control problems could be studied. In general a differential equation or boundary value problem is used to define a class of admissible functions, and then the problem is that of finding the extrema of a given functional defined on that class of functions.

scholarly journals On the existence of optimal control for controlled stochastic partial differential equations

1989 ◽  
Vol 115 ◽  
pp. 73-85 ◽  
Author(s):  
Noriaki Nagase
Keyword(s):  
Partial Differential Equations ◽  
Differential Operator ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Admissible Control ◽  
Order Differential Operator ◽  
Control Problems ◽  
Partial Differential ◽  
The Cauchy Problem ◽  
Existence Of Optimal Control

In this paper we are concerned with stochastic control problems of the following kind. Let Y(t) be a d’-dimensional Brownian motion defined on a probability space (Ω, F, Ft, P) and u(t) an admissible control. We consider the Cauchy problem of stochastic partial differential equations (SPDE in short)where L(y, u) is the 2nd order elliptic differential operator and M(y) the 1st order differential operator.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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