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Volume 13
Issue 9
10.3390/axioms13090575
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations

by
Nian Liu
School of Science, Wuhan University of Technology, Wuhan 430070, China
Axioms 2024, 13(9), 575; https://doi.org/10.3390/axioms13090575
Submission received: 24 July 2024 / Revised: 15 August 2024 / Accepted: 18 August 2024 / Published: 23 August 2024
(This article belongs to the Special Issue Differential Equations and Related Topics, 2nd Edition)
Versions Notes

Abstract

This article discusses the initial boundary value problem for a class of coupled systems of semi-linear pseudo-parabolic equations on a bounded smooth domain. Global solutions with exponential decay and asymptotic behavior are obtained when the maximal existence time has a lower bound for both low and overcritical energy cases. A sharp condition linking these phenomena is derived, and it is demonstrated that global existence also applies to the case of the potential well family.
Keywords: coupled pseudo-parabolic equations; uniform stabilization; asymptotic behavior; maximal existence time coupled pseudo-parabolic equations; uniform stabilization; asymptotic behavior; maximal existence time

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MDPI and ACS Style

Liu, N. Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations. Axioms 2024, 13, 575. https://doi.org/10.3390/axioms13090575

AMA Style

Liu N. Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations. Axioms. 2024; 13(9):575. https://doi.org/10.3390/axioms13090575

Chicago/Turabian Style

Liu, Nian. 2024. "Uniform Stabilization and Asymptotic Behavior with a Lower Bound of the Maximal Existence Time of a Coupled System’s Semi-Linear Pseudo-Parabolic Equations" Axioms 13, no. 9: 575. https://doi.org/10.3390/axioms13090575

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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