Neumann boundary condition for a non-autonomous Hamilton-Jacobi equation in a quarter plane

Adimurthi () and G. D. Veerappa Gowda ()
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Adimurthi: T.I.F.R. Centre for Applicable Mathematics
G. D. Veerappa Gowda: T.I.F.R. Centre for Applicable Mathematics

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 1, 199-224

Abstract: Abstract We consider Hamilton-Jacobi equation u t +H(u, u x ) = 0 in the quarter plane and study initial boundary value problems with Neumann boundary condition on the line x = 0. We assume that p → H(u, p) is convex, positively homogeneous of degree one. In general, this problem need not admit a continuous viscosity solution when s → H(s, p) is non increasing. In this paper, explicit formula for a viscosity solution of the initial boundary value problem is given for the cases s → H(s, p) is non decreasing as well as s → H(s, p) is non increasing.

Keywords: Hamilton-Jacobi equation; viscosity solution; Neumann boundary condition (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s13226-010-0001-5

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