Global Cauchy problems for hyperbolic systems with characteristics admitting superlinear growth for \( |x|\rightarrow \infty \)

DOI10.1016/j.crma.2008.11.009zbMath1194.35246OpenAlexW1972821458MaRDI QIDQ1000652

Daniel Gourdin, Todor Gramchev

Publication date: 10 February 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2008.11.009

zbMATH Keywords

weighted Sobolev spacesfinite propagation speedinstant blow-upfinite domains of dependence

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

The Continuity of Solutions with Respect to a Parameter to Symmetric Hyperbolic Systems ⋮ Cauchy problems for hyperbolic systems in \(\mathbb{R}^n\) with irregular principal symbol in time and for \(x \rightarrow \infty \) ⋮ Global Cauchy problems on \(\mathbb{R}^n\) for weakly hyperbolic systems with coefficients admitting superlinear growth for \(| x| \rightarrow \infty\) ⋮ Weak solutions of the cohomological equation on \(\mathbb R^2\) for regular vector fields

Cites Work

• Global solutions of a linear Cauchy problem.
• Cauchy problem for SG-hyperbolic equations with constant multiplicities
• Global in time solutions of evolution equations in scales of Banach function spaces in \(\mathbb R^n\)
• Probleme de cauchy non caracteristique pour les systemes hyperboliques a caracteristiques de multiplicite variable domaine de dependance
• Global L ²-Boundedness Theorems for a Class of Fourier Integral Operators
• The Non-Local Existence Problem of Ordinary Differential Equations
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