Singular perturbation and initial layer for the abstract Moore-Gibson-Thompson equation

被引:3
作者
Alvarez, Edgardo [1 ]
Lizama, Carlos [2 ]
机构
[1] Univ Norte, Dept Matemat & Estadist, Barranquilla, Colombia
[2] Univ Santiago Chile, Fac Ciencia, Dept Matemdt & Ciencia Comp, Las Sophoras 173, Santiago, Chile
关键词
Singular perturbation; Initial layer; Moore-Gibson-Thompson equation; Strongly continuous cosine family; Convergence; INTEGRODIFFERENTIAL EQUATIONS; DIFFERENTIAL-EQUATION; RELAXATION LIMIT; BOUNDARY-LAYER; CAUCHY; CONTROLLABILITY;
D O I
10.1016/j.jmaa.2022.126507
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We investigate the singular limit of a third-order abstract equation in time, in relation to the complete second-order Cauchy problem on Banach spaces, where the principal operator is the generator of a strongly continuous cosine family. Assuming that an initial datum is ill prepared, the initial layer problem is studied. We show convergence, which is uniform on compact sets that stay away from zero, as long as initial data are sufficiently smooth. Our method employs suitable results from the theory of general resolvent families of operators. The abstract formulation of the third-order in time equation is inspired by the Moore-Gibson-Thompson equation, which is the linearization of a model that currently finds applications in the propagation of ultrasound waves, displacement of certain viscoelastic materials, flexible structural systems that possess internal damping and the theory of thermoelasticity. (c) 2022 Elsevier Inc. All rights reserved.
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页数:21
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