Penalization for a PDE with a nonlinear Neumann boundary condition and measurable coefficients
Keyword(s):
We consider a system of semilinear partial differential equations (PDEs) with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized PDEs, which converges to our initial problem. Since the coefficients we consider may be discontinuous, we use the notion of solution in the [Formula: see text]-viscosity sense. The method we use is based on backward stochastic differential equations and their [Formula: see text]-tightness. This work is motivated by the fact that many PDEs in physics have discontinuous coefficients. As a consequence, it follows that if the uniqueness holds, then the solution can be constructed by a penalization.
1976 ◽
Vol 30
(133)
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pp. 68-68
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Keyword(s):
Layered stable equilibria of a reaction–diffusion equation with nonlinear Neumann boundary condition
2008 ◽
Vol 347
(1)
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pp. 123-135
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2008 ◽
Vol 48
(11)
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pp. 2077-2080
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2012 ◽
Vol 29
(3)
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pp. 778-798
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