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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 2
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Articles

On inverse initial value problems for the stochastic strongly damped wave equation

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Pages 527-544 | Received 16 Mar 2020, Accepted 30 Mar 2020, Published online: 15 Apr 2020
 

Abstract

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.

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No potential conflict of interest was reported by the author(s).

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