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Generalized solutions to a non Lipschitz- Cauchy problem

Devoue V.

Journal of Applied Analysis

2009

Vol. 15, nr 1

1-32

In this article we investigate solutions to a semilinear partial differential equation with non Lipschitz nonlinearity by using recent theories of generalized functions. To give a meaning to a non Lipschitz characteristic Cauchy problem with irregular data, we replace it by a three parameter family of problems. The first parameter turns the problem into a family of Lipschitz problems, the second one converts the given problem to a non-characteristic one, whereas the third one regularizes the data. Finally, the family of problems is solved in an appropriate three parametric (C,Ε,P) algebra.