Preprint 2003-049

Neumann Boundary Condition for Hamilton Jacobi Equation in a Quarter Plane

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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Author(s):

Adimurthi, <aditi@math.tifrbng.res.in>

G.D.Veerappa Gowda, <gowda@math.tifrbng.res.in>

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<aditi@math.tifrbng.res.in> July 26 2003.