Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recovering the initial condition of parabolic equations from lateral
  Cauchy data via the quasi-reversibility method   We consider the problem of computing the initial condition for a general
parabolic equation from the Cauchy lateral data. The stability of this problem
is well-known to be logarithmic. In this paper, we introduce an approximate
model, as a coupled linear system of elliptic partial differential equations.
The solution to this model is the vector of Fourier coefficients of the
solutions to the parabolic equation above. This approximate model is solved by
the quasi-reversibility method. We will prove the convergence for the
quasi-reversibility method as the measurement noise tends to 0. The convergent
rate is Lipschitz. We present the implementation of our algorithm in details
and verify our method by showing some numerical examples.

27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat