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