Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6891825 | Computers & Mathematics with Applications | 2018 | 18 Pages |
Abstract
We focus on a inverse source problem in a partial differential equation containing a fractional derivative in time of the order 1<β<2. The equation is accompanied with a non-standard boundary condition which consists of the classic flux term and the dynamical time-fractional derivative term on the one part of the boundary. To determine both the solution of the equation and the source term, a measurement in a form of a integral over space domain is considered. Using a time-discretization and Rothe's method, we prove an existence of the strong solution in the suitable functional spaces, and the error estimate is established; moreover, the uniqueness is addressed. The results are supported by some numerical experiments.
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Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
K. Å iÅ¡ková, M. SlodiÄka,