Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Initial-boundary value and inverse problems for subdiffusion equations
  in $\mathbb{R}^N$   An initial-boundary value problem for a subdiffusion equation with an
elliptic operator $A(D)$ in $\mathbb{R}^N$ is considered. The existence and
uniqueness theorems for a solution of this problem are proved by the Fourier
method. Considering the order of the Caputo time-fractional derivative as an
unknown parameter, the corresponding inverse problem of determining this order
is studied. It is proved, that the Fourier transform of the solution
$\hat{u}(\xi, t)$ at a fixed time instance recovers uniquely the unknown
parameter. Further, a similar initial-boundary value problem is investigated in
the case when operator $A(D)$ is replaced by its power $A^\sigma$. Finally, the
existence and uniqueness theorems for a solution of the inverse problem of
determining both the orders of fractional derivatives with respect to time and
the degree $ \sigma $ are proved. We also note that when solving the inverse
problems, a decrease in the parameter $\rho$ of the Mettag-Leffler functions
$E_\rho$ has been proved.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th