By means of convenient regularization for an ill posed Cauchy problem, we deï¬ne an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with data given on a characteristic curve, we...

This article adresses questions on localization and microlocalization in the framework of the so called (C,E,P)–algebras of generalized functions. We give new results on nonlinear properties of the asymptotic singular spectrum in the multi-parameter case, a tool to describe the singularities...

We extend classical results from the Colombeau algebra, concerning point-value characterizations of generalized functions, to the more general case of multi-parameter (C,E,P)–algebras. Our investigations include considerations about different definitions of subspaces related to tempered...

By means of convenient regularizations for an ill posed Cauchy problem, we define an associated generalized problem and discuss the conditions for the solvability of it. To illustrate this, starting from the semilinear unidirectional wave equation with non Lipschitz nonlinearity and irregular...