EXISTENCE AND UNIQUENESS OF SOLUTION OF FIRST ORDER QUASILINEAR HYPERBOLIC SYSTEM IN TWO INDEPENDENT VARIABLES USING FIXED POINT THEORMS

Abstract

Let A(t, x, u) u_t + B(t, x, u) u_x = C(t, x, u) be a strictly hyperbolic n x n system with u(0, x) = f(x) its initial data. Using the relative compactibility of the domain of dependence of solution, the contraction mapping principle and Schauder fixed point theorem, the existence and uniqueness of the solution to the Cauchy problem are established.


Key Words: Uniqueness, Strict Hyperbolicity, Compact and Contraction Operator.


Global Jnl of Mathematical Sciences Vol. 31) 2004: 5-10