Initial-boundary value problem for a nonlinear wave equation with strong damping and structural damping

Jiaxin Xu; Shubin Wang; Xuelian Chen; Jiaxin Xu; Shubin Wang; Xuelian Chen

doi:10.3934/math.2026825

AIMS Mathematics

2026, Volume 11, Issue 7: 20309-20337. doi: 10.3934/math.2026825

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Research article

Initial-boundary value problem for a nonlinear wave equation with strong damping and structural damping

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Received: 20 May 2026 Revised: 24 June 2026 Accepted: 26 June 2026 Published: 10 July 2026
MSC : 35G31, 35L05, 35L30

In this paper, we are concerned with an initial boundary value problem of wave equations incorporating strong damping and structural damping. By virtue of semigroup theory, we establish the global well-posedness of weak solutions, where the nonlinear damping and source terms satisfy subcritical growth conditions. Furthermore, based on Nakao's inequality, we derive the exponential decay estimate of solutions. Notably, we relax the constraints on the coefficients of structural damping to a general non-negativity condition.
- wave equation,
- nonlinear damping,
- well-posedness,
- decay rates
Citation: Jiaxin Xu, Shubin Wang, Xuelian Chen. Initial-boundary value problem for a nonlinear wave equation with strong damping and structural damping[J]. AIMS Mathematics, 2026, 11(7): 20309-20337. doi: 10.3934/math.2026825

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Abstract

In this paper, we are concerned with an initial boundary value problem of wave equations incorporating strong damping and structural damping. By virtue of semigroup theory, we establish the global well-posedness of weak solutions, where the nonlinear damping and source terms satisfy subcritical growth conditions. Furthermore, based on Nakao's inequality, we derive the exponential decay estimate of solutions. Notably, we relax the constraints on the coefficients of structural damping to a general non-negativity condition.

References

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