Regularity properties, representation of solutions and spectral asymptotics of systems with multiplicities

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dc.creatorKamotski, Ilia
dc.creatorRuzhansky, Michael
dc.date2004-02-12
dc.date.accessioned2026-07-07T09:18:39Z
dc.date.available2026-07-07T09:18:39Z
dc.descriptionProperties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral operators. It is shown that this series is an asymptotic expansion with respect to smoothness under quite general geometric conditions. Propagation of singularities and sharp regularity properties of solutions are obtained. Results are applied to establish regularity estimates for scalar weakly hyperbolic equations with involutive characteristics. They are also applied to derive the first and second terms of spectral asymptotics for the corresponding elliptic systems.
dc.identifierhttps://arxiv.org/abs/math/0402203
dc.identifierhttp://arxiv.org/abs/math/0402203
dc.identifierComm. Partial Differential Equations, 32 (2007), 1-35.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/154101
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject35S30, 35L45, 35L30, 35C20, 58J40
dc.titleRegularity properties, representation of solutions and spectral asymptotics of systems with multiplicities
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