AN UNDETERMINED TIME-DEPENDENT COEFFICIENT IN A FRACTIONAL DIFFUSION EQUATION

作者：Zhang Zhidong^*

来源：Inverse Problems and Imaging, 2017, 11(5): 875-900.

DOI：10.3934/ipi.2017041

• Fractional diffusion
• fractional inverse problem
• uniqueness
• existence
• monotonicity
• iteration algorithm

In this work, we consider a FDE (fractional diffusion equation)
(C)D(t)(alpha)u(x, t) - a(t)Lu(x, t) = F(x, t)
with a time-dependent diffusion coefficient a(t). This is an extension of [I which deals with this FDE in one-dimensional space. For the direct problem, given an a(t), we establish the existence, uniqueness and some regularity properties with a more general domain Omega and right-hand side F(x,t). For the inverse problem recovering a(t), we introduce an operator K one of whose fixed points is a(t) and show its monotonicity, uniqueness and existence of its fixed points. With these properties, a reconstruction algorithm for a(t) is created and some numerical results are provided to illustrate the theories.

• 出版日期2017-10