Approximation of the initial value for damped nonlinear hyperbolic equations with random Gaussian white noise on the measurements
The main goal of this work is to study a regularization method to reconstruct the solution of the backward non-linear hyperbolic equation $ u_{tt} + \alpha\Delta^2u_t +\beta \Delta ^2u = \mathcal{F}(x, t, u) $ come with the input data are blurred by random Gaussian white noise. We first prove that t...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2022-04-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://aimspress.com/article/doi/10.3934/math.2022698?viewType=HTML |