Approximate controllability of stochastic integrodifferential system with nonlocal condition

The aim of this article is to investigate the existence of mild solutions as well as approximate controllability of non-autonomous Sobolev type differential equations with the nonlocal condition. To prove our results, we will take the help of Krasnoselskii fixed point technique, evolution system and controllability of the corresponding linear system.

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Approximate Controllability of Semilinear Stochastic Integrodifferential System with Nonlocal Conditions

Fractal and Fractional ◽

10.3390/fractalfract2040029 ◽

2018 ◽

Vol 2 (4) ◽

pp. 29 ◽

Cited By ~ 1

Author(s):

Annamalai Anguraj ◽

K. Ramkumar

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Point Theorem ◽

Hilbert Spaces ◽

Approximate Controllability ◽

Nonlocal Conditions ◽

Initial Condition ◽

Nonlocal Initial Condition ◽

Integrodifferential System ◽

Physical Phenomena

The objective of this paper is to analyze the approximate controllability of a semilinear stochastic integrodifferential system with nonlocal conditions in Hilbert spaces. The nonlocal initial condition is a generalization of the classical initial condition and is motivated by physical phenomena. The results are obtained by using Sadovskii’s fixed point theorem. At the end, an example is given to show the effectiveness of the result.

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Exact and Approximate Controllability for Distributed Parameter Systems

10.1017/cbo9780511721595 ◽

2008 ◽

Cited By ~ 75

Author(s):

Roland Glowinski ◽

Jacques-Louis Lions ◽

Jiwen He

Keyword(s):

Approximate Controllability ◽

Distributed Parameter Systems ◽

Distributed Parameter

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Hypothesis on the Solvability of Parabolic Equations with nonlocal Condition

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2002.7.1.15204 ◽

2002 ◽

Vol 7 (1) ◽

pp. 93-104 ◽

Cited By ~ 10

Author(s):

Mifodijus Sapagovas

Keyword(s):

Parabolic Equation ◽

Parabolic Equations ◽

Existence And Uniqueness ◽

Nonlocal Condition ◽

Nonlocal Conditions ◽

Numerical Algorithms ◽

Uniqueness Of The Solution

Numerous and different nonlocal conditions for the solvability of parabolic equations were researched in many articles and reports. The article presented analyzes such conditions imposed, and observes that the existence and uniqueness of the solution of parabolic equation is related mainly to ”smallness” of functions, involved in nonlocal conditions. As a consequence the hypothesis has been made, stating the assumptions on functions in nonlocal conditions are related to numerical algorithms of solving parabolic equations, and not to the parabolic equation itself.

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