First-order hyperbolic pseudodifferential equations with generalized symbols

DOI10.1016/j.jmaa.2003.12.013zbMath1057.35111arXivmath/0307406OpenAlexW2106286861MaRDI QIDQ1827066

Günther Hörmann

Publication date: 6 August 2004

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

Full work available at URL: https://arxiv.org/abs/math/0307406

zbMATH Keywords

generalized solutionColombeau algebrahyperbolic pseudodifferential Cauchy problem

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Initial value problems for first-order hyperbolic systems (35L45) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (13)

Notes on regularity results in Colombeau algebras ⋮ Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems ⋮ Symmetric hyperbolic systems in algebras of generalized functions and distributional limits ⋮ Wave Equations and Symmetric First-order Systems in Case of Low Regularity ⋮ GENERALIZED SOLUTIONS FOR THE EULER–BERNOULLI MODEL WITH ZENER VISCOELASTIC FOUNDATIONS AND DISTRIBUTIONAL FORCES ⋮ Generalized Fourier Integral Operator Methods for Hyperbolic Equations with Singularities ⋮ Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients ⋮ Hyperbolic Systems with Discontinuous Coefficients: Generalized Wavefront Sets ⋮ Generalized Fourier Integral Operators on Spaces of Colombeau Type ⋮ On Local and Global Regularity of Fourier Integral Operators ⋮ Generalized solutions for the Euler-Bernoulli model with distributional forces ⋮ Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory ⋮ Topological structures in Colombeau algebras: Investigation of the duals of \(\mathcal G_c(\Omega)\), \(\mathcal G(\Omega)\) and \(\mathcal G_{\mathcal S}(\mathbb R^n)\)

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