Electron. J. Diff. Eqns., Vol. 2008(2008), No. 157, pp. 1-8.

Explicit solutions for a system of first-order partial differential equations

Kayyunnapara Thomas Joseph

Abstract:
In this paper we construct explicit weak solutions of a system of two partial differential equations in the quarter plane $\{(x,t):x>0,t>0\}$ with initial conditions at $t=0$ and a weak form of Dirichlet boundary conditions at $x=0$. This system was first studied by LeFloch [9], where he constructed explicit formula for the weak solution of pure initial value problem.

Submitted November 1, 2008. Published November 20, 2008.
Math Subject Classifications: 35A20, 35L50, 35R05.
Key Words: First order equations; boundary conditions; exact solutions

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Kayyunnapara Thomas Joseph
School of Mathematics
Tata Institute of Fundamental Research
Homi Bhabha Road
Mumbai 400005, India
email: ktj@math.tifr.res.in

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