Problème de Cauchy semi-linéaire en 3 dimensions d'espace. Un résultat de finitude. (A semilinear Cauchy problem in three dimensional spaces. A finiteness result)
type: Item
instance of: scholarly article
title: Problème de Cauchy semi-linéaire en 3 dimensions d'espace. Un résultat de finitude. (A semilinear Cauchy problem in three dimensional spaces. A finiteness result)
zbMATH Open document ID: 0648.35057
DOI: 10.1016/0022-1236(88)90138-3
author: Gilles Lebeau
published in: Journal of Functional Analysis
publication date: 1988-01-01T00:00:00Z
review text: We prove that if u is a solution of the semilinear wave equation \[ (\partial^ 2_ t-\Delta)u=\sum_{0\leq j\leq j_ 0}p_ j(t,x)u^ j,\quad (t,x)\in {\mathbb{R}}^ 4,\quad u\in H^ s,\quad s>2, \] such that the Cauchy data of u, \(u|_{t=0}\), \((\partial u/\partial t)|_{t=0}\) are Hörmander Fourier integral distributions on some analytic Lagrangian, then for every real \(\sigma\), there exist a subanalytic homogeneous isotropic subset \(L_{\sigma}\) of \(T^*{\mathbb{R}}^ 4\) such that \(WF^{\sigma}(u)\subset L_{\sigma}\). In particular, for every integer k, u is \(C^ k\) on a dense open subset.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35A27
zbMATH DE Number: 4058071
zbMATH Keywords: semilinear
zbMATH Keywords: Cauchy data
zbMATH Keywords: integral distributions
zbMATH Keywords: subanalytic homogeneous isotropic subset
MaRDI profile type: Publication
full work available at URL: 0022-1236(88)90138-3
OpenAlex ID: W2031168854
cites work: Self-spreading and strength of singularities for solutions to semilinear wave equations
cites work: Q3963412
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description: scientific article; zbMATH DE number 4058071