Regularity Properties, Representation of Solutions, and Spectral Asymptotics of Systems with Multiplicities

DOI10.1080/03605300600856816zbMath1132.35055arXivmath/0402203OpenAlexW2035983264MaRDI QIDQ3436028

Michael Ruzhansky, Ilia V. Kamotski

Publication date: 8 May 2007

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

Full work available at URL: https://arxiv.org/abs/math/0402203

zbMATH Keywords

Duhamel's principlePicard iteration schemevariable multiplicitymicrolocal diagonazibilitymulti-phase Fourier integral operators

Mathematics Subject Classification ID

Pseudodifferential and Fourier integral operators on manifolds (58J40) Initial value problems for first-order hyperbolic systems (35L45) Fourier integral operators applied to PDEs (35S30) Singularity in context of PDEs (35A21)

Related Items (16)

Hyperbolic systems with non-diagonalisable principal part and variable multiplicities. I: Well-posedness ⋮ The spectral function of a first order elliptic system ⋮ Multidimensional van der Corput-type estimates involving Mittag-Leffler functions ⋮ On \(C^\infty\) well-posedness of hyperbolic systems with multiplicities ⋮ Inhomogeneous wave equation with \(t\)-dependent singular coefficients ⋮ The second Weyl coefficient for a first order system ⋮ Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters ⋮ Non-commutative harmonic oscillators and related problems ⋮ Local-in-space criteria for blowup in shallow water and dispersive rod equations ⋮ On Local and Global Regularity of Fourier Integral Operators ⋮ Van der Corput lemmas for Mittag-Leffler functions. II: \(\alpha\)-directions ⋮ Hyperbolic systems with non-diagonalisable principal part and variable multiplicities, II: microlocal analysis ⋮ Cauchy Problem for Some 2 × 2 Hyperbolic Systems of Pseudo-differential Equations with Nondiagonalisable Principal Part ⋮ On the wave equation with multiplicities and space-dependent irregular coefficients ⋮ Weyl asymptotics for tensor products of operators and Dirichlet divisors ⋮ Recent progress in elliptic equations and systems of arbitrary order with rough coefficients in Lipschitz domains

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