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Research Article | Open Access

Continuous dependence on initial data and high energy blowup time estimate for porous elastic system

Jiangbo Han1, Runzhang Xu1, Chao Yang1,2( )
College of Mathematical Sciences, Harbin Engineering University, 150001, Harbin, People's Republic of China
Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland
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Abstract

In this paper, we establish two conclusions about the continuous dependence on the initial data of the global solution to the initial boundary value problem of a porous elastic system for the linear damping case and the nonlinear damping case, respectively, which reflect the decay property of the dissipative system. Additionally, we estimate the lower bound of the blowup time at the arbitrary positive initial energy for nonlinear damping case.

Keywords

porous elastic systemcontinuous dependenceblowup timearbitrary positive initial energy
CLC number: 35L53, 35B30, 35B44

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Communications in Analysis and Mechanics
Volume 15 Issue 2,
June 2023
Pages 214-244
DOI: 10.3934/cam.2023012

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Cite this article:
Han J, Xu R, Yang C. Continuous dependence on initial data and high energy blowup time estimate for porous elastic system. Communications in Analysis and Mechanics, 2023, 15(2): 214-244. https://doi.org/10.3934/cam.2023012

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Received: 10 April 2023
Revised: 22 May 2023
Accepted: 22 May 2023
Published: 15 June 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)