Improved decay of solution for strongly damped nonlinear wave equations

Yongbing Luo; Yongbing Luo

doi:10.3934/mbe.2023225

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4865-4876. doi: 10.3934/mbe.2023225

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Improved decay of solution for strongly damped nonlinear wave equations

Yongbing Luo ^,

College of Mathematics and Computer Science, Zhejiang A&F University, Zhejiang 311300, China

Academic Editor: Weining Wu

Received: 20 October 2022 Revised: 02 December 2022 Accepted: 20 December 2022 Published: 04 January 2023

In this work, we deal with the initial boundary value problem of solutions for a class of linear strongly damped nonlinear wave equations $ u_{tt}-\Delta u -\alpha \Delta u_t = f(u) $ in the frame of a family of potential wells. For this strongly damped wave equation, we not only prove the global-in-time existence of the solution, but we also improve the decay rate of the solution from the polynomial decay rate to the exponential decay rate.
- wave equations,
- linear strong damping,
- global existence,
- decay
Citation: Yongbing Luo. Improved decay of solution for strongly damped nonlinear wave equations[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4865-4876. doi: 10.3934/mbe.2023225

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Abstract

In this work, we deal with the initial boundary value problem of solutions for a class of linear strongly damped nonlinear wave equations $ u_{tt}-\Delta u -\alpha \Delta u_t = f(u) $ in the frame of a family of potential wells. For this strongly damped wave equation, we not only prove the global-in-time existence of the solution, but we also improve the decay rate of the solution from the polynomial decay rate to the exponential decay rate.

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