STUDY OF NONLINEAR WAVE EQUATION WITH SINGULAR DATA BY USING GENERALIZED FIXED POINT.

The paper is devoted to proving an existence and uniqueness result for generalized solution to a class of nonlinear wave equations in space dimensions d = 1 , 2 , 3 . It is shown that for a nonlinearity of f and arbitrary growth and sign, which depends on the time variable and parameter, the initial value problem for the linear wave equation has a unique solution in a Colombeau subalgebra of bounded type. The proof is based on a fixed point theorem in an ultrametric topology on a closed subspace of these subalgebras. The results presented generalize and unify several existing results in the literature. [ABSTRACT FROM AUTHOR]