Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximation of a degenerate semilinear PDEs with a nonlinear Neumann
  boundary condition   We consider a system of semilinear partial differential equations (PDEs) with
a nonlinearity depending on both the solution and its gradient. The Neumann
boundary condition depends on the solution in a nonlinear manner. The uniform
ellipticity is not required to the diffusion coefficient. We show that this
problem admits a viscosity solution which can be approximated by a
penalization. The Lipschitz condition is required to the coefficients of the
diffusion part. The nonlinear part as well as the Neumann condition are
Lipschitz. Moreover, the nonlinear part is assumed monotone in the solution
variable. Note that the existence of a viscosity solution to this problem has
been established in [13] then completed in [15]. In the present paper, We
construct a sequence of penalized system of decoupled forward backward
stochastic differential equations (FBSDEs) then we directly show its strong
convergence. This allows us to deal with the case where the nonlinearity
depends on both the solution and its gradient. Our work extends, in particular,
the result of [4] and, in some sense, those of [1, 3]. In contrast to works [1,
3, 4], we do not pass by the weak compactness of the laws of the stochastic
system associated to our problem.

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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga