The growth or decay estimates for nonlinear wave equations with damping and source terms

Peng Zeng; Dandan Li; Yuanfei Li; Peng Zeng; Dandan Li; Yuanfei Li

doi:10.3934/mbe.2023623

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 13989-14004. doi: 10.3934/mbe.2023623

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The growth or decay estimates for nonlinear wave equations with damping and source terms

School of Data Science, Guangzhou Huashang College, Guangdong 511300, China

Academic Editor: Sheldon Wang

Received: 26 February 2023 Revised: 17 May 2023 Accepted: 01 June 2023 Published: 21 June 2023

The spatial decay or growth behavior of a coupled nonlinear wave equation with damping and source terms is considered. By defining the wave equations in a cylinder or an exterior region, the spatial growth and decay estimates for the solutions are obtained by assuming that the boundary conditions satisfy certain conditions. We also show that the growth or decay rates are faster than those obtained by relevant literature. This kind of spatial behavior can be extended to a nonlinear system of viscoelastic type. In the case of decay, we also prove that the total energy can be bounded by known data.
- wave equations,
- spatial behavior,
- viscoelastic type,
- total energies
Citation: Peng Zeng, Dandan Li, Yuanfei Li. The growth or decay estimates for nonlinear wave equations with damping and source terms[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 13989-14004. doi: 10.3934/mbe.2023623

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Abstract

The spatial decay or growth behavior of a coupled nonlinear wave equation with damping and source terms is considered. By defining the wave equations in a cylinder or an exterior region, the spatial growth and decay estimates for the solutions are obtained by assuming that the boundary conditions satisfy certain conditions. We also show that the growth or decay rates are faster than those obtained by relevant literature. This kind of spatial behavior can be extended to a nonlinear system of viscoelastic type. In the case of decay, we also prove that the total energy can be bounded by known data.

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