Quasiasymptotic analysis in Colombeau algebra (Q1763403)
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scientific article; zbMATH DE number 2136271
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Quasiasymptotic analysis in Colombeau algebra |
scientific article; zbMATH DE number 2136271 |
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Quasiasymptotic analysis in Colombeau algebra (English)
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22 February 2005
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The notions of quasiasymptotic and \(S\)-asymptotic behaviour and expansion have been well developed in the spaces of generalized functions (distributions, ultradistributions, hyperfunctions, etc.). The present paper treats the problem how to apply the quasiasymptotics and the \(S\)-asymptotics to the Colombeau algebra. The authors take into account applications to nonlinear partial differential equations and integral equations as well. The examples are of significant interest themselves. The present paper is highly recommended to all specialists interested in the asymptotical behaviour of solutions to nonlinear mathematical models.
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Colombeau algebra of generalized functions
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\(\mathcal G\)-q.a. behavior at zero
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semilinear hyperbolic system
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\(\mathcal G\)-q.a. expansion at infinity
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wave equation
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\(Sc\)-asymptotic
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\(Sc\)-boundedness
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semilinear parabolic equations
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\(Sc\)-asymptotic expansion
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0.8834337
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0.8816103
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0.8680234
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0.8653679
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