# Approximate Controllability for a Semilinear Stochastic Evolution System with Infinite Delay in $$L_p$$ L p Space

Approximate Controllability for a Semilinear Stochastic Evolution System with Infinite Delay in... In this paper, approximate controllability for a class of infinite-delayed semilinear stochastic systems in $$L_p$$ L p space ( $$2<p<\infty$$ 2 < p < ∞ ) is studied. The fundamental solution’s theory is used to describe the mild solution which is obtained by using the Banach fixed point theorem. In this way the approximate controllability result is then obtained by assuming that the corresponding deterministic linear system is approximately controllable via the so-called the resolvent condition. An application to a Volterra stochastic equation is also provided to illustrate the obtained results. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

# Approximate Controllability for a Semilinear Stochastic Evolution System with Infinite Delay in $$L_p$$ L p Space

, Volume 75 (2) – Feb 11, 2016
31 pages

/lp/springer_journal/approximate-controllability-for-a-semilinear-stochastic-evolution-Cm0VfuwU0J
Publisher
Springer US
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-016-9332-x
Publisher site
See Article on Publisher Site

### Abstract

In this paper, approximate controllability for a class of infinite-delayed semilinear stochastic systems in $$L_p$$ L p space ( $$2<p<\infty$$ 2 < p < ∞ ) is studied. The fundamental solution’s theory is used to describe the mild solution which is obtained by using the Banach fixed point theorem. In this way the approximate controllability result is then obtained by assuming that the corresponding deterministic linear system is approximately controllable via the so-called the resolvent condition. An application to a Volterra stochastic equation is also provided to illustrate the obtained results.

### Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Feb 11, 2016

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