Filter regularization for an inverse parabolic problem in several variables
Tuan, Nguyen Huy
Long, Le Dinh
Nguyen, Thinh Van
Texas State University, Department of Mathematics
The backward heat problem is known to be ill possed, which has lead to the design of several regularization methods. In this article we apply the method of filtering out the high frequencies from the data for a parabolic equation. First we identify two properties that if satisfied they imply the convergence of the approximate solution to the exact solution. Then we provide examples of filters that satisfy the two properties, and error estimates for their approximate solutions. We also provide numerical experiments to illustrate our results.
Ill-posed problem, Truncation method, Heat equation, Regularization
Tuan, N. H., Kirane, M., Le, L. D., & Nguyen, T. V. (2016). Filter regularization for an inverse parabolic problem in several variables. <i>Electronic Journal of Differential Equations, 2016</i>(24), pp. 1-13.