Quasiasymptotic analysis in Colombeau algebra

DOI10.1016/j.jmaa.2004.07.044zbMath1067.46040OpenAlexW2013091892MaRDI QIDQ1763403

Stevan Pilipović, Mirjana Stojanovic

Publication date: 22 February 2005

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2004.07.044

zbMATH Keywords

wave equationsemilinear parabolic equationssemilinear hyperbolic systemColombeau algebra of generalized functions\(\mathcal G\)-q.a. behavior at zero\(\mathcal G\)-q.a. expansion at infinity\(Sc\)-asymptotic\(Sc\)-asymptotic expansion\(Sc\)-boundedness

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Second-order nonlinear hyperbolic equations (35L70) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Cites Work

• A nonlinear theory of generalized functions.
• Generalized solution to a semilinear hyperbolic system with a non-Lipschitz nonlinearity
• Semilinear parabolic equations with singular initial data in anisotropic weighted spaces
• \(\mathcal G\)-quasiasymptotics at infinity
• Semi-linear wave equations
• Generalized solutions to nonlinear Volterra integral equations with non-Lipschitz nonlinearity
• Reflection of delta-waves for nonlinear wave equations in one space variable
• Parabolic equations with conservative nonlinear term and singular initial data
• A Calculus Approach to Hyperfunctions. II
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