Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Lizama, Carlos¹  Zamorano, Sebastian¹ 

[1] Univ Santiago Chile, Fac Ciencia, Dept Matemat & Ciencia Comp, Sophoras 173, Santiago, Chile

关键词: Null controllability;    Moore-Gibson-Thompson equation;    Observability inequality;    Moving control;    Implicit function theorem;   

DOI  :  10.1016/j.jde.2018.12.017

来源: Elsevier

【 摘 要 】

We show that the Moore-Gibson-Thomson equation tau partial derivative(ttt) y+ alpha partial derivative(tt) y - c(2)Delta y - b Delta partial derivative(t) y = K partial derivative(tt) (y(2) ) + chi(omega)(t)(u), is controlled by a force that is supported on an moving subset omega (t) of the domain, satisfying a geometrical condition. Using the concept of approximately outer invertible map, a generalized implicit function theorem and assuming that gamma := alpha-tau c(2)/b 0, the local null controllability in the nonlinear case is established. Moreover, the analysis of the critical value gamma = 0 for the linear equation is included. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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