Recovering the initial distribution for strongly damped wave equation

Authors: Nguyễn Huy Tuấn, Võ Văn Âu, Daniel Lesnic, Vuong Nguyen Doan, Nguyễn Huy Tuấn,

https://www.sciencedirect.com/science/article/abs/pii/S0893965917301271?via%3Dihub

Publisher, magazine: ,

Publication year: 2017

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Abstract

We study for the first time the inverse backward problem for the strongly damped wave equation. First, we show that the problem is severely ill-posed in the sense of Hadamard. Then, under the a priori assumption on the exact solution belonging to a Gevrey space, we propose the Fourier truncation method for stabilizing the ill-posed problem. A stability estimate of logarithmic type is established.

Tags: Fourier regularization method, Final value problem, Strongly damped wave equation