Generalized solutions to a semilinear wave equation

Semilinear wave equations in space dimension n ⩽ 9 with singular data and various types of nonlinearities are considered. We employ the framework of the algebra G L 2 of generalized functions. In the general case, the nonlinear term is regularized with respect to a small parameter ε such that it becomes globally Lipschitz for each such ε . This produces a family of Cauchy problems, to which we construct a family of solutions which in turn determines an element of G L 2 which serves as a generalized solution to the original equation. For cubic nonlinear terms the equation is directly solved in G L 2 without regularizations. Finally, in certain cases, it is shown that the solution to the regularized equation coincides with the solution to the nonregularized one.