Division problem and partial differential equations with constant coefficients in Colombeau's space of new generalized functions

Abstract

We study the problem of division in Colombeau's space of new generalized functions in the associated sense: more precisely we solve the equation of the form F·G ≈ pH with adequate assumptions on F. By using the Fourier transformation we construct, by simple methods, the solution in the p-associated sense of a partial differential equation with constant coefficients.