Semilinear hyperbolic equations
type: Item
instance of: scholarly article
title: Semilinear hyperbolic equations
zbMATH Open document ID: 0959.35002
author: Vladimir Georgiev
published in: MSJ Memoirs
publication date: 2001-02-15T00:00:00Z
full work available at URL: http://projecteuclid.org/euclid.msjm/1416320829
review text: The aim of the lecture note is to explain how to derive sharp a priori estimates which enable one to prove a global in time existence of solutions to semilinear wave equations and nonlinear Klein-Gordon equations. The first chapters contain some basic facts of functional analysis, interpolation theorems, Fourier transform on hyperboloid, weighted Sobolev spaces of fractional order and pseudodifferential operators. The core of the work is devoted to Fourier transform on manifolds of constant negative curvature and sharp \(L^p\)-weighted a priori estimates of solutions to wave and Klein-Gordon equations. Global existence and asymptotic behaviour of the solutions of Cauchy problems for semilinear wave and Klein-Gordon equations with small initial data are proved in the last chapter. The lecture note is useful for graduate students as well as for specialists in the field of partial differential equations.
reviewed by: Marie Kopáčková
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 35B45
Mathematics Subject Classification ID: 43A15
Mathematics Subject Classification ID: 43A85
zbMATH DE Number: 1565319
zbMATH Keywords: sharp a priori estimates
zbMATH Keywords: Klein-Gordon equation
zbMATH Keywords: semilinear wave equation
zbMATH Keywords: Fourier transform
zbMATH Keywords: weighted Sobolev space of fractional order
zbMATH Keywords: global in time existence of solutions
zbMATH Keywords: manifolds of constant negative curvature
zbMATH Keywords: small initial data
MaRDI profile type: Publication
OpenAlex ID: W1492475323
DOI: 10.2969/MSJMEMOIRS/007020000
description: scientific article; zbMATH DE number 1565319