TY - JOUR
AU - Gurefe, Yusuf
AU - Le, Dinh Long
AU - Kumar, Devendra
PY - 2023/05/08
Y2 - 2024/07/15
TI - Regularization of nonlocal pseudo-parabolic equation with random noise
JF - Electronic Journal of Applied Mathematics
JA - Electron. J. Appl. Math.
VL - 1
IS - 1
SE - Research Article
DO - 10.61383/ejam.20231119
UR - https://ejamjournal.com/index.php/ejam/article/view/ejam.20231119
SP - 40-61
AB - <p><span class="fontstyle0">In this paper, we consider an inverse problem for a time-fractional diffusion equation with the inhomogeneous source. These problems have many applications in engineering such as image processing, geophysics, biology. We get the result in random case as follows:</span></p><p><span class="fontstyle0">• This problem is ill-posed.</span></p><p><span class="fontstyle0">• We have used the nonlocal condition, instead of the final time condition.</span></p><p><span class="fontstyle0">• Using the IFT regularization method, constructing the regularized solution, the a-priori choice rule </span><span class="fontstyle0">for the regularization parameter is discussed and yields the corresponding convergence rate.</span></p><p><span class="fontstyle0">• A numerical experiment is presented to illustrate the results in theory.</span></p>
ER -