Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and error estimates of a general modified quasi-boundary value
  method via a semi-linear backward parabolic equation   Regularization methods have been recently developed to construct stable
approximate solutions to classical partial differential equations considered as
final value problems. In this paper, we investigate the backward parabolic
problem with locally Lipschitz source:
$\partial_{t}u+\mu\left(t\right)\mathcal{A}u\left(t\right)=f\left(t,u\right)$
where
$\mathcal{A}:\mathcal{D}\left(\mathcal{A}\right)\subset\mathcal{H}\to\mathcal{H}$
is a positive, self-adjoint and unbounded linear operator on the Hilbert space
$\mathcal{H}$. The problem arises in many applications, but it is in general
ill-posed. The ill-posedness is caused by catastrophic growth in the
representation of solution, then independence of solution on data makes
computational procedures impossible. Therefore, we contribute to this
interesting field the study of the stable approximation solution via the
modified quasi-boundary value method based on nonlinear spectral theory, which
slightly extends the results in many works. Our main focus is to qualitatively
prove the stability and convergence rate where semi-group technicalities are
highly useful.

26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom