Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rigorous numerics of blow-up solutions for ODEs with exponential
  nonlinearity   Our concerns here are blow-up solutions for ODEs with exponential
nonlinearity from the viewpoint of dynamical systems and their numerical
validations. As an example, the finite difference discretization of $u_t =
u_{xx} + e^{u^m}$ with the homogeneous Dirichlet boundary condition is
considered. Our idea is based on compactification of phase spaces and
time-scale desingularization as in previous works. In the present case,
treatment of exponential nonlinearity is the main issue. Fortunately, under a
kind of exponential homogeneity of vector field, we can treat the problem in
the same way as polynomial vector fields. In particular, we can characterize
and validate blow-up solutions with their blow-up times for differential
equations with such exponential nonlinearity in the similar way to previous
works. A series of technical treatments of exponential nonlinearity in blow-up
problems is also shown with concrete validation examples.

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The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics