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Research Article | Open Access

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

Jiaxin Xu( ), Shubin Wang, Xuelian Chen
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China
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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.

Keywords

wave equationnonlinear dampingwell-posednessdecay rates
CLC number: 35G31, 35L05, 35L30

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AIMS Mathematics
Volume 11 Issue 7,
July 2026
Pages 20309-20337
DOI: 10.3934/math.2026825

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Cite this article:
Xu J, Wang S, Chen X. Initial-boundary value problem for a nonlinear wave equation with strong damping and structural damping. AIMS Mathematics, 2026, 11(7): 20309-20337. https://doi.org/10.3934/math.2026825

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Received: 20 May 2026
Revised: 24 June 2026
Accepted: 26 June 2026
Published: 15 July 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)