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On prouve que le problème de Cauchy local pour l’équation d’onde sur-critique dans $ℝ^{d}$ , $□ u + u^{p} = 0$ , $p$ impair, avec $d \geq 3$ et $p > (d + 2) / (d - 2)$ , est mal posé dans $H^{σ}$ pour tout $σ \in] 1, σ_{crit} [$ , où $σ_{crit} = d / 2 - 2 / (p - 1)$ est l’exposant critique.

Pointwise controllability as limit of internal controllability for the wave equation in one space dimension.

Fabre, Caroline, Puel, Jean-Pierre (1994)

Portugaliae Mathematica

Pointwise decay for solutions of the 2D Neumann exterior problem for the wave equation. II

Paolo Secchi (2002)

Rendiconti del Seminario Matematico della Università di Padova

Pointwise Fourier Inversion: a Wave Equation Approach.

Mark A. Pinsky, Michael E. Taylor (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Pointwise Fourier Inversion on Tori and Other Compact Manifolds.

Michael Taylor (1999)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Probabilistic well-posedness for the cubic wave equation

Nicolas Burq, Nikolay Tzvetkov (2014)

Journal of the European Mathematical Society

The purpose of this article is to introduce for dispersive partial differential equations with random initial data, the notion of well-posedness (in the Hadamard-probabilistic sense). We restrict the study to one of the simplest examples of such equations: the periodic cubic semi-linear wave equation. Our contributions in this work are twofold: first we break the algebraic rigidity involved in our previous works and allow much more general randomizations (general infinite product measures v.s. Gibbs...

Problème spectrale concernant l'opérateur de Laplace et les domaines des polyèdres générés par le systéme de racines de type C.

P. T. Craciunas, D. L. Fernández, D. Magueron, A. F. Shestopal (1985)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Propagation des ondes dans les dièdres

G. Lebeau (1992/1993)

Séminaire Équations aux dérivées partielles (Polytechnique)

Propagation des ondes dans les dièdres

Gilles Lebeau (1995)

Mémoires de la Société Mathématique de France

Propagation des ondes dans les variétés à coins

Gilles Lebeau (1997)

Annales scientifiques de l'École Normale Supérieure

Propagation et réflexion de la propriété de transmission des distributions de Fourier

Alain Piriou (1977)

Journées équations aux dérivées partielles

Propagation of singularities for the wave equation on manifolds with corners

András Vasy (2004/2005)

Séminaire Équations aux dérivées partielles

In this talk we describe the propagation of $𝒞^{\infty}$ and Sobolev singularities for the wave equation on $𝒞^{\infty}$ manifolds with corners $M$ equipped with a Riemannian metric $g$ . That is, for $X = M \times ℝ_{t}$ , $P = D_{t}^{2} - Δ_{M}$ , and $u \in H_{loc}^{1} (X)$ solving $P u = 0$ with homogeneous Dirichlet or Neumann boundary conditions, we show that ${WF}_{b} (u)$ is a union of maximally extended generalized broken bicharacteristics. This result is a $𝒞^{\infty}$ counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary,...

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