A source identification problem in a time-fractional wave equation with a dynamical boundary condition

作者：Siskova K; Slodicka M^*

来源：Computers & Mathematics with Applications, 2018, 75(12): 4337-4354.

DOI：10.1016/j.camwa.2018.03.033

• Time-fractional wave equation
• Dynamical boundary condition
• Inverse source problem
• Reconstruction
• Convergence
• Time discretization

We focus on a inverse source problem in a partial differential equation containing a fractional derivative in time of the order 1 < beta < 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.

• 出版日期2018-6-15