Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative estimates of unique continuation for parabolic equations,
  determination of unknown time-varying boundaries and optimal stability
  estimates   In this paper we will review the main results concerning the issue of
stability for the determination unknown boundary portion of a thermic
conducting body from Cauchy data for parabolic equations. We give detailed and
selfcontained proofs. We prove that such problems are severely ill-posed in the
sense that under a priori regularity assumptions on the unknown boundaries, up
to any finite order of differentiability, the continuous dependence of unknown
boundary from the measured data is, at best, of logarithmic type.

0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci