Improved decay of solution for strongly damped nonlinear wave equations
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Updated: Aug 7, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
1College of Mathematics and Computer Science, Zhejiang A&F University, Zhejiang 311300, China.
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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