Nonlinear maps in spaces of distributions (Q805994)
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scientific article; zbMATH DE number 4205141
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Nonlinear maps in spaces of distributions |
scientific article; zbMATH DE number 4205141 |
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Nonlinear maps in spaces of distributions (English)
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1992
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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.
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nonlinear superposition
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strongly singular distributions
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\(\sigma \) - ultradistribution
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Cauchy problems for a class of semilinear hyperbolic systems in space dimension one with singular initial data
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\(\sigma \) - Colombeau algebra
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