Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 157, pp. 1-8.

Title: Explicit solutions for a system of first-order 
       partial differential equations
   
Author: Kayyunnapara Thomas Joseph (Tata Institutei, Mumbai, India)

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