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Division problem and partial differential equations with constant coefficients in Colombeau’s space of new generalized functions. (English) Zbl 0868.35017
Summary: 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 \(F\cdot G\approx_pH\) 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.

MSC:
35E05 Fundamental solutions to PDEs and systems of PDEs with constant coefficients
26C10 Real polynomials: location of zeros
46F05 Topological linear spaces of test functions, distributions and ultradistributions
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