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

Jiangbo Han; Runzhang Xu; Chao Yang; Jiangbo Han; Runzhang Xu; Chao Yang

doi:10.3934/cam.2023012

Communications in Analysis and Mechanics

2023, Volume 15, Issue 2: 214-244. doi: 10.3934/cam.2023012

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Research article

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

1.
College of Mathematical Sciences, Harbin Engineering University, 150001, Harbin, People's Republic of China
2.
Faculty of Applied Mathematics, AGH University of Science and Technology, 30-059 Kraków, Poland

Received: 10 April 2023 Revised: 22 May 2023 Accepted: 22 May 2023 Published: 01 June 2023
35L53, 35B30, 35B44

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.
- porous elastic system,
- continuous dependence,
- blowup time,
- arbitrary positive initial energy
Citation: Jiangbo Han, Runzhang Xu, Chao Yang. Continuous dependence on initial data and high energy blowup time estimate for porous elastic system[J]. Communications in Analysis and Mechanics, 2023, 15(2): 214-244. doi: 10.3934/cam.2023012

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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.

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