Boundary feedback stabilization of a critical nonlinear JMGT equation with Neumann-undissipated part of the boundary

Author:

Bongarti Marcelo1,Lasiecka Irena2

Affiliation:

1. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10777, Berlin, Germany

2. Department of Mathematical Sciences, University of Memphis, 3725 Norriswood Ave, Memphis, TN 38152, United States, IBS, Polish Academy of Sciences, Warsaw

Abstract

<p style='text-indent:20px;'>Boundary feedback stabilization of a <i>critical</i> third–order (in time) semilinear Jordan–Moore–Gibson–Thompson (JMGT) is considered. The word <i>critical</i> here refers to the usual case where media–damping effects are non–existent or non–measurable and therefore cannot be relied upon for stabilization purposes. Motivated by modeling aspects in high-intensity focused ultrasound (HIFU) technology, the boundary feedback under consideration is supported only on a portion of the boundary. At the same time, the remaining part is undissipated and subject to Neumann/Robin boundary conditions. As such, unlike Dirichlet, it fails to satisfy the Lopatinski condition, a fact which compromises tangential regularity on the boundary [<xref ref-type="bibr" rid="b37">37</xref>]. In such a configuration, the analysis of uniform stabilization from the boundary becomes subtle and requires careful geometric considerations and microlocal analysis estimates. The nonlinear effects in the model demand construction of suitably small solutions which are invariant under the dynamics. The assumed smallness of the initial data is required only at the lowest energy level topology, which is sufficient to construct sufficiently smooth solutions to the nonlinear model.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

Cited by 1 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Moore‐Gibson‐Thompson heat conduction equation for non centrosymmetric rigid solids;ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik;2023-10-04

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