Mathematical Methods in the Applied Sciences

RESEARCH ARTICLE

Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data

Corresponding Author

Yuta Wakasugi

[email protected]

orcid.org/0000-0001-9807-7927

Laboratory of Mathematics, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527 Japan

Correspondence

Yuta Wakasugi, Laboratory of Mathematics, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan.

Email: [email protected]

Communicated by: M. Reissig

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Yuta Wakasugi,

Corresponding Author

Yuta Wakasugi

[email protected]

orcid.org/0000-0001-9807-7927

Laboratory of Mathematics, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527 Japan

Correspondence

Yuta Wakasugi, Laboratory of Mathematics, Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima 739-8527, Japan.

Email: [email protected]

Communicated by: M. Reissig

Search for more papers by this author

First published: 06 January 2023

https://doi.org/10.1002/mma.8957

Citations: 1

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Abstract

We study the large time behavior of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity in the whole space or exterior domains. Our result shows how the amplitude of the damping coefficient, the power of the nonlinearity, and the decay rate of the initial data at the spatial infinity determine the decay rates of the energy and the ${L}^2$ -norm of the solution. In the appendix, we also give a survey of basic results on the local and global existence of solutions and the properties of weight functions used in the energy method.

CONFLICT OF INTEREST

This work does not have any conflict of interest.

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Volume46, Issue6

April 2023

Pages 7067-7107

Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data

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Decay property of solutions to the wave equation with space-dependent damping, absorbing nonlinearity, and polynomially decaying data

Abstract

CONFLICT OF INTEREST

REFERENCES

Citing Literature

References

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