Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity

Enrico Bernardi; Antonio Bove; Vesselin Petkov

Displaying similar documents to “Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity”

$L^{p}$ - $L^{q}$ -Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity

Jerzy Gawinecki (1991)

Annales Polonici Mathematici

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We prove the $L^{p}$ - $L^{q}$ -time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the $L^{p}$ - $L^{q}$ -time decay estimates.

On a linear hyperbolic equation with smooth coefficients without solutions

Yuri Egorov (1996)

Banach Center Publications

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An example of a locally unsolvable hyperbolic equation of the second order is constructed, which has smooth ( $C^{\infty}$ ) coefficients, but has no solutions in the class of distributions.

Hyperbolic angle function in the Lorentzian plane

Emilija Nešović (2005)

Kragujevac Journal of Mathematics

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Anisotropic Hölder and Sobolev spaces for hyperbolic diffeomorphisms

Viviane Baladi, Masato Tsujii (2007)

Annales de l’institut Fourier

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We study spectral properties of transfer operators for diffeomorphisms $T : X \to X$ on a Riemannian manifold $X$ . Suppose that $Ω$ is an isolated hyperbolic subset for $T$ , with a compact isolating neighborhood $V \subset X$ . We first introduce Banach spaces of distributions supported on $V$ , which are anisotropic versions of the usual space of $C^{p}$ functions $C^{p} (V)$ and of the generalized Sobolev spaces $W^{p, t} (V)$ , respectively. We then show that the transfer operators associated to $T$ and a smooth weight $g$ extend boundedly to these...

Nonlocal problem for the hyperbolic system of differential equation of the first order.

Zarȩba, Lech (2001)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

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Oblique derivative problem for elliptic equations in non-divergence form with $V M O$ coefficients

Giuseppe di Fazio, Dian K. Palagachev (1996)

Commentationes Mathematicae Universitatis Carolinae

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A priori estimates and strong solvability results in Sobolev space $W^{2, p} (Ω)$ , $1 < p < \infty$ are proved for the regular oblique derivative problem $\{\begin{matrix} \sum_{i, j = 1}^{n} a^{i j} (x) \frac{\partial^{2} u}{\partial x_{i} \partial x_{j}} = f (x) a.e. Ω \\ \frac{\partial u}{\partial ℓ} + σ (x) u = ϕ (x) on \partial Ω \end{matrix}$ when the principal coefficients $a^{i j}$ are $V M O \cap L^{\infty}$ functions.

Contact geometry of hyperbolic equations of generic type.

The, Dennis (2008)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

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On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and $ℤ_{p}$ the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, $k_{\infty}$ a $ℤ_{p}$ -extension of k, $k_{n}$ the nth layer of $k_{\infty} / k$ , and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ . Iwasawa proved the following well-known theorem about the order $A_{n}$ of $A_{n}$ : Theorem A (Iwasawa). Let $k_{\infty} / k$ be a $ℤ_{p}$ -extension and $A_{n}$ the p-Sylow subgroup of the ideal class group of $k_{n}$ , where $k_{n}$ is the $n$ th layer of $k_{\infty} / k$ . Then there exist integers $λ = λ (k_{\infty} / k) \geq 0$ , $μ = μ (k_{\infty} / k) \geq 0$ , $ν = ν (k_{\infty} / k)$ , and n₀ ≥ 0...

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...