Geometric transition for a class of hyperbolic operators with double characteristics

Bernardi, Enrico; Bove, Antonio

doi:10.4099/math1924.23.1

Cited by 6 publications

(1 citation statement)

References 13 publications

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“…The case (i) in Theorem 1.2, namely e(ρ) ≡ 0 on Σ was proved in [4] while in [15], it was proved under less restrictive assumption, the non existence of bicharacteristics tangent to S. The case (ii) in Theorem 1.2 and hence µ(ρ) ≡ 0 on Σ, was proved in [16]. Some transition cases from effectively hyperbolic to non-effectively hyperbolic are studied in [3,1,5]. In particular in [1,5] a typical case of (iii) was studied but the condition (1.4) was not investigated.…”

Section: Introductionmentioning

confidence: 99%

On the Cauchy Problem for Differential Operators with Double Characteristics, A Transition from Non-effective to Effective Characteristics

Nishitani

2018

Publ. Res. Inst. Math. Sci.

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We discuss the well-posedness of the Cauchy problem for hyperbolic operators with double characteristics which changes from non-effectively hyperbolic to effectively hyperbolic, on the double characterisitic manifold, across a submanifold of codimension 1. We assume that there is no bicharacteristic tangent to the double characteristic manifold and the spatial dimension is 2. Then we prove the well-posedness of the Cauchy problem in all Gevrey classes assuming, on the double characteristic manifold, that the ratio of the imaginary part of the subprincipal symbol to the real eigenvalue of the Hamilton map is bounded and that the sum of the real part of the subprincipal symbol and the modulus of the imaginary eigenvalue of the Hamilton map is strictly positive.

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Section: Introductionmentioning

confidence: 99%

On the Cauchy Problem for Differential Operators with Double Characteristics, A Transition from Non-effective to Effective Characteristics

Nishitani

2018

Publ. Res. Inst. Math. Sci.

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On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case

Nishitani

2013

Progress in Nonlinear Differential Equations and Their Applications

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On the Cauchy Problem for Hyperbolic Operators with Double Characteristics

Parenti¹,

Parmeggiani²

2012

Evolution Equations of Hyperbolic and Schrödinger Type

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Geometric transition for a class of hyperbolic operators with double characteristics

Cited by 6 publications

References 13 publications

On the Cauchy Problem for Differential Operators with Double Characteristics, A Transition from Non-effective to Effective Characteristics

On the Cauchy Problem for Differential Operators with Double Characteristics, A Transition from Non-effective to Effective Characteristics

On the Cauchy Problem for Noneffectively Hyperbolic Operators, a Transition Case

On the Cauchy Problem for Hyperbolic Operators with Double Characteristics

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