Results from the now-classical distribution theory involving convolution and Fourier
transformation are extended to cater for Colombeau's generalized functions. Indications are …

Starting from a locally convex metrisable topological space and from any asymptotic scale,
we construct a generalized extension of this space. To those extensions, we associate …

Nonlinear algebraic analysis of delta shock wave solutions to Burgers' equation Page 1 Pacific
Journal of Mathematics NONLINEAR ALGEBRAIC ANALYSIS OF DELTA SHOCK WAVE …

JF Colombeau and other authors have introduced algebras of generalized functions in order
to solve differential problems which have no solution in spaces of distributions. These …

The usual properties of generalized functions are described by means of two fundamental
structures. With those structures we can construct in a general way a sheaf A of differential …

We discuss various methods of regularization of singular differential problems. Their
common point is that we use the flexibility of the theories of nonlinear generalized functions …

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 …

We introduce different notions of wave front set for the functionals in the dual of the
Colombeau algebra $\Gc (\Om) $ providing a way to measure the $\G $ and the $\Ginf …

We show that a well-defined generalized problem can be associated, in the framework of (𝒞,
ℰ, 𝒫)-algebras, with an ill-posed one (with singular data, singular coefficients or in the …

In this paper we investigate solutions to the semi-linear wave equation in canonical form
with non Lipschitz non-linearity and distributions or other generalized functions as data. To …