Approximate Controllability of the System Governed by Double Coupled Semilinear Degenerate Parabolic Equations
Year: 2020
Author: Chunpeng Wang, Fengdan Xu, Qian Zhou
Communications in Mathematical Research , Vol. 36 (2020), Iss. 4 : pp. 403–422
Abstract
This paper concerns the approximate controllability of the initial-boundary problem of double coupled semilinear degenerate parabolic equations. The equations are degenerate at the boundary, and the control function acts in the interior of the spacial domain and acts only on one equation. We overcome the difficulty of the degeneracy of the equations to show that the problem is approximately controllable in $L^2$ by means of a fixed point theorem and some compact estimates. That is to say, for any initial and desired data in $L^2$, one can find a control function in $L^2$ such that the weak solution to the problem approximately reaches the desired data in $L^2$ at the terminal time.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cmr.2020-0061
Communications in Mathematical Research , Vol. 36 (2020), Iss. 4 : pp. 403–422
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Double coupled degeneracy approximate controllability.