Nonlinear maps in spaces of distributions
One studies nonlinear superposition F(u) for certain strongly singular distributions u. It turns out that for analytic maps F(u) is a \(\sigma\)- ultradistribution and an effective link between the index \(\sigma\) and the strength of the singularity of u is established. An application to the Cauchy problems for a class of semilinear hyperbolic systems in space dimension one with singular initial data is proposed and construction of \(\sigma\)-Colombeau algebra is given.
Cauchy problems for a class of semilinear hyperbolic systems in space dimension one with singular initial data
scientific article; zbMATH DE number 4205141
scientific article