Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Existence, blow-up and exponential decay estimates for a nonlinear wave
  equation with boundary conditions of two-point type   This paper is devoted to study a nonlinear wave equation with boundary
conditions of two-point type. First, we state two local existence theorems and
under suitable conditions, we prove that any weak solutions with negative
initial energy will blow up in finite time. Next, we give a sufficient
condition to guarantee the global existence and exponential decay of weak
solutions. Finally, we present numerical results

29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn