Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension

Asma Azaiez; Nader Masmoudi; Hatem Zaag

doi:10.1017/9781108367639.001

Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension

Asma Azaiez, Nader Masmoudi, Hatem Zaag

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in H¹ _loc × L² _loc or sometimes in W^1,∞ × L^∞, we derive the blow-up rate near a non-characteristic point in the smaller space, and give some bounds near other points. Our results generalize those proved by Godin under high regularity assumptions on initial data.

Original language	English (US)
Title of host publication	Partial Differential Equations Arising from Physics and Geometry
Subtitle of host publication	A Volume in Memory of Abbas Bahri
Publisher	Cambridge University Press
Pages	1-32
Number of pages	32
ISBN (Electronic)	9781108367639
ISBN (Print)	9781108431637
DOIs	https://doi.org/10.1017/9781108367639.001
State	Published - Jan 1 2019

ASJC Scopus subject areas

General Mathematics

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abstract = "We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in H1 loc × L2 loc or sometimes in W1,∞ × L∞, we derive the blow-up rate near a non-characteristic point in the smaller space, and give some bounds near other points. Our results generalize those proved by Godin under high regularity assumptions on initial data.",

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Blow-up rate for a semilinear wave equation with exponential nonlinearity in one space dimension

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