Volume 298, Issue 2 pp. 478-510

ORIGINAL ARTICLE

Decay character and global existence for weakly coupled system of semilinear $\sigma$ -evolution damped equations with time-dependent damping

Cung The Anh,

Cung The Anh

Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

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Phan Duc An,

Phan Duc An

Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

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Pham Trieu Duong,

Corresponding Author

Pham Trieu Duong

[email protected]

orcid.org/0000-0002-4351-5237

Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

Correspondence

Pham Trieu Duong, Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam.

Email: [email protected]

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Cung The Anh,

Cung The Anh

Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

Search for more papers by this author

Phan Duc An,

Phan Duc An

Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

Search for more papers by this author

Pham Trieu Duong,

Corresponding Author

Pham Trieu Duong

[email protected]

orcid.org/0000-0002-4351-5237

Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam

Correspondence

Pham Trieu Duong, Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy, Hanoi, Vietnam.

Email: [email protected]

Search for more papers by this author

First published: 27 November 2024

https://doi.org/10.1002/mana.202400243

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Abstract

In this article, we investigate the existence and decay rate of the global solution to the coupled system of semilinear structurally damped $\sigma$ -evolution equations with time-dependent damping in the so-called effective cases

\begin{equation*} \hspace*{7pc}{\begin{cases} u_{t t}+(-\Delta)^{\sigma _1} u+b_1(t) (-\Delta)^{\delta _1} u_t=|v_t|^p, \\ v_{t t}+(-\Delta)^{\sigma _2} v+b_2(t) (-\Delta)^{\delta _2} v_t=|u_t|^q. \end{cases}} \end{equation*}

We obtain conditions for the existence and the decay estimates of the global (in time) solution that are expressed in terms of the decay character of the initial data

u_0(x)=u(0, x), \nobreakspace v_0(x)=v(0, x)

and

u_1(x)=u_t(0, x),\nobreakspace v_1(x)=v_t(0, x)

. Furthermore, the blow-up results for solutions to the semilinear problem also presented.

CONFLICT OF INTEREST STATEMENT

The authors declare no conflicts of interest.

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Volume298, Issue2

February 2025

Pages 478-510

Decay character and global existence for weakly coupled system of semilinear $\sigma$ -evolution damped equations with time-dependent damping

Abstract

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Decay character and global existence for weakly coupled system of semilinear σ $\sigma$ -evolution damped equations with time-dependent damping

Abstract

CONFLICT OF INTEREST STATEMENT

REFERENCES

References

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Decay character and global existence for weakly coupled system of semilinear $\sigma$ -evolution damped equations with time-dependent damping