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

Adimurthi, ; Veerappa Gowda, G. D. (2010) Neumann boundary condition for a non-autonomous Hamilton-Jacobi equation in a quarter plane Indian Journal of Pure and Applied Mathematics, 41 (1). pp. 199-224. ISSN 0019-5588

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Official URL: http://www.springerlink.com/index/K4375N2M42723H8T...

Related URL: http://dx.doi.org/10.1007/s13226-010-0001-5

Abstract

We consider Hamilton-Jacobi equation ut+H(u, ux ) = 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.

Item Type:Article
Source:Copyright of this article belongs to Indian National Science Academy.
Keywords:Hamilton-Jacobi Equation; Viscosity Solution; Neumann Boundary Condition
ID Code:11834
Deposited On:13 Nov 2010 13:47
Last Modified:16 May 2016 21:15

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