Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniqueness from pointwise observations in a multi-parameter inverse
  problem   In this paper, we prove a uniqueness result in the inverse problem of
determining several non-constant coefficients of one-dimensional
reaction-diffusion equations. Such reaction-diffusion equations include the
classical model of Kolmogorov, Petrovsky and Piskunov as well as more
sophisticated models from biology. When the reaction term contains an unknown
polynomial part of degree $N,$ with non-constant coefficients $\mu_k(x),$ our
result gives a sufficient condition for the uniqueness of the determination of
this polynomial part. This sufficient condition only involves pointwise
measurements of the solution $u$ of the reaction-diffusion equation and of its
spatial derivative $\partial u / \partial x$ at a single point $x_0,$ during a
time interval $(0,\epsilon).$ In addition to this uniqueness result, we give
several counter-examples to uniqueness, which emphasize the optimality of our
assumptions. Finally, in the particular cases N=2 and $N=3,$ we show that such
pointwise measurements can allow an efficient numerical determination of the
unknown polynomial reaction term.

16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics