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.

**Paper:**- Available as PostScript (656 Kbytes) or gzipped PostScript (208 Kbytes; uncompress using gunzip).
**Author(s):**- Adimurthi, <aditi@math.tifrbng.res.in>
- G.D.Veerappa Gowda, <gowda@math.tifrbng.res.in>
**Publishing information:****Comments:****Submitted by:**- <aditi@math.tifrbng.res.in> July 26 2003.

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