Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Identification of time-varying source term in time-fractional diffusion
  equations   This paper is concerned with the inverse problem of determining the time and
space dependent source term of diffusion equations with constant-order
time-fractional derivative in $(0,2)$. We examine two different cases. In the
first one, the source is the product of two spatial and temporal terms, and we
prove that both of them can be retrieved by knowledge of one arbitrary internal
measurement of the solution for all times. In the second case, we assume that
the first term of the product varies with one fixed space variable, while the
second one is a function of all the remaining space variables and the time
variable, and we show that both terms are uniquely determined by two arbitrary
lateral measurements of the solution over the entire time span. These two
source identification results boil down to a weak unique continuation principle
in the first case and a unique continuation principle for Cauchy data in the
second one, that are preliminarily established. Finally, numerical
reconstruction of spatial term of source terms in the form of the product of
two spatial and temporal terms, is carried out through an iterative algorithm
based on the Tikhonov regularization method.

28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an