Preprint 2003-049

Neumann Boundary Condition for Hamilton Jacobi Equation in a Quarter Plane

Adimurthi and G.D.Veerappa Gowda

Abstract: We consider Hamilton Jacobi equation $u_{t} + H(u,u_{x})$ in the quarter plane and study the initial boundary value problem on the line x=0. We obtain explicit formulas for the viscosity solution when p -> H(u,p) is convex and positively homogenous of degree $m /geq 1$. If m=1 and s->H(s,p) is nonincreasing, in general, this problem need not admits a continuous viscosity solution. Even in this case, we obtain explicit formula for discontinuous viscosity solutions.

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Adimurthi, <>
G.D.Veerappa Gowda, <>
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