Recovering the initial distribution for strongly damped wave equation
https://www.sciencedirect.com/science/article/abs/pii/S0893965917301271?via%3DihubPublisher, magazine: ,
Publication year: 2017
Lưu Trích dẫn Chia sẻAbstract
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
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