The cauchy problem for weakly hyperbolic equation

DOI10.1080/03605308008820132zbMath0452.35078OpenAlexW2042749059MaRDI QIDQ3898891

Hitoshi Uryu

Publication date: 1980

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308008820132

zbMATH Keywords

Cauchy problemwell-posednessweakly hyperbolic operatorsnon- involutive multiple characteristics

Mathematics Subject Classification ID

Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for higher-order hyperbolic equations (35L30)

Related Items (9)

Generalized Levi conditions for weakly hyperbolic equations. An attempt to treat the degeneracy with respect to the space variables ⋮ A necessary and sufficient condition for the well-posedness of some weakly hyperbolic cauchy problems ⋮ Branching of singularities for degenerate hyperbolic operators and Stokes phenomena. II ⋮ Non—uniqueness in the cauchy problem for partial differential operators with chatacteristics I ⋮ Fundamental solution for a hyperbolic system with diagonal principal part ⋮ Fundamental solution for a hyperbolic equation with involutive characteristics of variable multiplicity ⋮ On energy inequalities and regularity of solutions to weakly hyperbolic Cauchy problems ⋮ Well posedness in the C∞ class for utt=a(u)Δu ⋮ Conditions for well-posedness in Gevrey classes of the Cauchy problems for Fuchsian hyperbolic operators

Cites Work

• Opérateurs hyperboliques à caractéristiques de multiplicité constante
• The correctness of the Cauchy problem
• On cauchy's problem for partial differential equations with multiple characteristics
• The Cauchy Problem for Weakly Hyperbolic Equations
• The well-posedness of the cauchy problem for partial differential equations with multiple characteristics
• Multi—products ofphase functions for fourier integral opertaors with an application
• On the cauchy problem for weakly hyperbolic equations
• Sur la condition de E. E. Levi concernant des équations hyperboliques

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