Solvability of the Nonlocal Initial Value Problem and Application to Design of Controller for Heat-Equation with Delay

Solvability of the Nonlocal Initial Value Problem and Application to Design of Controller for Heat-Equation with Delay

Year:    2019

Author:    Xiao-Pei Liu, Gen-Qi Xu

Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 127–159

Abstract

In this paper, we study the solvability of a distribution-valued heat equation with nonlocal initial condition. Under proper assumption on parameters we get the explicit solution of the distribution-valued heat equation. As an application, we further consider the stabilization problem of heat equation with partial-delay in internal control. By the parameterization design of feedback controller, we show if the integral kernel functions are determined by the solution of the distribution heat equation with nonlocal initial value problem, then the closed-loop system can be transformed into a system which is called the target system of the exponential stability under the bounded linear transformation. By selecting different distribution-valued kernel functions, we give the inverse transformation. Hence the closed-loop system is equivalent to the target system.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v52n2.19.02

Journal of Mathematical Study, Vol. 52 (2019), Iss. 2 : pp. 127–159

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    33

Keywords:    Abstract heat equation Solvability nonlocal initial value condition internal delayed control integral-type feedback controller exponential stability.

Author Details

Xiao-Pei Liu

Gen-Qi Xu