Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perturbation Methods and First Order Partial Differential Equations   In this paper, we give explicit estimates that insure the existence of
solutions for first order partial differential operators on compact manifolds,
using a viscosity method. In the linear case, an explicit integral formula can
be found, using the characteristics curves. The solution is given explicitly on
the critical points and the limit cycles of the vector field of the first order
term of the operator. In the nonlinear case, a generalization of the
Weitzenbock formula provides pointwise estimates that insure the existence of a
solution, but the uniqueness question is left open. Nevertheless we prove that
uniqueness is stable under a C^{1} perturbation. Finally, we give some examples
where the solution fails to exist globally, justifying the need to impose
conditions that warrant global existence. The last result reveals that the zero
order term in the first order operator is necessary to obtain generically
bounded solutions.

17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
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The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol