Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-sided estimates of the solution set for the reaction-diffusion
  problem with uncertain data   We consider linear reaction--diffusion problems with mixed
Diriclet-Neumann-Robin conditions. The diffusion matrix, reaction coefficient,
and the coefficient in the Robin boundary condition are defined with an
uncertainty which allow bounded variations around some given mean values. A
solution to such a problem cannot be exactly determined (it is a function in
the set of "possible solutions" formed by generalized solutions related to
possible data). The problem is to find parameters of this set. In this paper,
we show that computable lower and upper bounds of the diameter (or radius) of
the set can be expressed throughout problem data and parameters that regulate
the indeterminacy range. Our method is based on using a posteriori error
majorants and minorants of the functional type (see monographs
Neittaanm\"aki&Repin 2004, Repin 2008), which explicitly depend on the
coefficients and allow to obtain the corresponding lower and upper bounds by
solving the respective extremal problems generated by indeterminacy of
coefficients.

10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th