On the well-posedness of weakly hyperbolic equations with time-dependent coefficients

DOI10.1016/j.jde.2012.05.001zbMath1259.35133arXiv1107.2565OpenAlexW2963355372MaRDI QIDQ439103

Michael Ruzhansky, Claudia Garetto

Publication date: 1 August 2012

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.2565

zbMATH Keywords

ultradistributionsGevrey spaces

Mathematics Subject Classification ID

Topological linear spaces of test functions, distributions and ultradistributions (46F05) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items (18)

Hyperbolic systems with non-diagonalisable principal part and variable multiplicities. I: Well-posedness ⋮ Well-posedness of hyperbolic systems with multiplicities and smooth coefficients ⋮ On \(C^\infty\) well-posedness of hyperbolic systems with multiplicities ⋮ Weakly hyperbolic equations with non-analytic coefficients and lower order terms ⋮ Inhomogeneous wave equation with \(t\)-dependent singular coefficients ⋮ Wave equation for operators with discrete spectrum and irregular propagation speed ⋮ Gevrey functions and ultradistributions on compact Lie groups and homogeneous spaces ⋮ On the wave equation with space dependent coefficients: singularities and lower order terms ⋮ Non-local initial problem for second order time-fractional and space-singular equation ⋮ Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters ⋮ On hyperbolic equations and systems with non-regular time dependent coefficients ⋮ On hyperbolic systems with time-dependent Hölder characteristics ⋮ A note on weakly hyperbolic equations with analytic principal part ⋮ Time-dependent wave equations on graded groups ⋮ Discrete time-dependent wave equations. I. Semiclassical analysis ⋮ On the wave equation with multiplicities and space-dependent irregular coefficients ⋮ Wave equation for sums of squares on compact Lie groups ⋮ Hyperbolic second order equations with non-regular time dependent coefficients

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