On inverse initial value problems for the stochastic strongly damped wave equation
https://www.tandfonline.com/doi/abs/10.1080/00036811.2020.1751826?journalCode=gapa20Publisher, magazine: ,
Publication year: 2020
Lưu Trích dẫn Chia sẻAbstract
We consider two final value problem of a stochastic strongly damped wave equation driven by white noise (Section 3) and fractional noise (Section 4). We show that a stochastic integral in the solution is not stable and the problem is not well posed. To regularize the problem in two cases of noise, we apply the Fourier truncated method to control the frequency in such a way that it depends on the noisy level, which is the upper bound of the errors appearing in the input data. Furthermore, the convergence rate of the regularized solution is investigated.
Tags: Stochastic problem, inverse problem, strongly damped wave equation, regularization method
Các bài viết liên quan đến tác giả Tran Bao Ngoc
Regularization of a sideways problem for a time-fractional diffusion equation with nonlinear source
Existence and regularity of inverse problem for the nonlinear fractional Rayleigh-Stokes equations
On inverse initial value problems for the stochastic strongly damped wave equation
On a backward problem for nonlinear fractional diffusion equations
Existence and regularity of final value problems for time fractional wave equations
On well-posedness of the sub-diffusion equation with conformable derivative model