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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Univ Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, FranceUniv Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, France
Dekkers, Adrien
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Rozanova-Pierrat, Anna
Khodygo, Vladimir
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Aberystwyth Univ, Inst Biol Environm & Rural Sci, Penglais Campus, Aberystwyth SY23 3DA, Ceredigion, WalesUniv Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, France
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Univ Paris Saclay, Lab Math & Informat Complexite & Syst, Cent Supelec, Campus Gif Sur Yvette,3 Rue Joliot Curie, F-91190 Gif Sur Yvette, FranceUniv Paris Saclay, Lab Math & Informat Complexite & Syst, Cent Supelec, Campus Gif Sur Yvette,3 Rue Joliot Curie, F-91190 Gif Sur Yvette, France
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Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France
CNRS, IMB, UMR 5251, F-33400 Talence, FranceUniv Bordeaux, IMB, UMR 5251, F-33400 Talence, France
Ducrot, Arnaud
Magal, Pierre
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Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France
CNRS, IMB, UMR 5251, F-33400 Talence, FranceUniv Bordeaux, IMB, UMR 5251, F-33400 Talence, France
Magal, Pierre
Seydi, Ousmane
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Ecole Polytech Thies, Dept Tronc Commun, Thies, SenegalUniv Bordeaux, IMB, UMR 5251, F-33400 Talence, France
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Univ Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, FranceUniv Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, France
Dekkers, Adrien
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Rozanova-Pierrat, Anna
Khodygo, Vladimir
论文数: 0引用数: 0
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Aberystwyth Univ, Inst Biol Environm & Rural Sci, Penglais Campus, Aberystwyth SY23 3DA, Ceredigion, WalesUniv Paris Saclay, Lab Math & Informat Complexite & Syst, CentraleSupelec, Campus Gif Sur Yvette, F-91190 Gif Sur Yvette 91190, France
机构:
Univ Paris Saclay, Lab Math & Informat Complexite & Syst, Cent Supelec, Campus Gif Sur Yvette,3 Rue Joliot Curie, F-91190 Gif Sur Yvette, FranceUniv Paris Saclay, Lab Math & Informat Complexite & Syst, Cent Supelec, Campus Gif Sur Yvette,3 Rue Joliot Curie, F-91190 Gif Sur Yvette, France
机构:
Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France
CNRS, IMB, UMR 5251, F-33400 Talence, FranceUniv Bordeaux, IMB, UMR 5251, F-33400 Talence, France
Ducrot, Arnaud
Magal, Pierre
论文数: 0引用数: 0
h-index: 0
机构:
Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France
CNRS, IMB, UMR 5251, F-33400 Talence, FranceUniv Bordeaux, IMB, UMR 5251, F-33400 Talence, France
Magal, Pierre
Seydi, Ousmane
论文数: 0引用数: 0
h-index: 0
机构:
Ecole Polytech Thies, Dept Tronc Commun, Thies, SenegalUniv Bordeaux, IMB, UMR 5251, F-33400 Talence, France