Controllability properties of degenerate pseudo-parabolic boundary control problems

Zhang Mu-Ming; Xu Tian-Yuan; Yin Jing-Xue

doi:10.3934/mcrf.2019034

Article Contents

2020, Volume 10, Issue 1: 157-169. Doi: 10.3934/mcrf.2019034

This issue Previous Article Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative Next Article A direct method based on the Clenshaw-Curtis formula for fractional optimal control problems

Controllability properties of degenerate pseudo-parabolic boundary control problems

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

^* Corresponding author: Tian-Yuan Xu
^* Corresponding author: Tian-Yuan Xu

Received: August 31, 2018

Revised: January 31, 2019

Early access: April 2019

Published: February 2020

The first author is supported by the China Postdoctoral Science Foundation grant 2018M630960, and the Excellent Young Scholar Program of South China Normal University grant 17KJ01. The second author is supported by the Joint Training PhD Program of China Scholarship Council grant 201806750016, and the Innovation Project of Graduate School of South China Normal University grant 2018LKXM005. The third author is supported by NSFC grant 11771156

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Abstract

This paper concerns with the boundary control of a degenerate pseudo-parabolic equation. Compare to the results those for degenerate parabolic equations, we discover that the null controllability property for the degenerate pseudo-parabolic equation is false, but the approximate controllability in some proper state space holds.

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Mathematics Subject Classification: Primary: 93B05, 93B07; Secondary: 35K10.

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