# Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

Mathematical Modelling of Natural Phenomena (2012)

- Volume: 7, Issue: 2, page 66-76
- ISSN: 0973-5348

## Access Full Article

top## Abstract

top## How to cite

topIbrahim, S., and Lyaghfouri, A.. "Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent." Mathematical Modelling of Natural Phenomena 7.2 (2012): 66-76. <http://eudml.org/doc/222260>.

@article{Ibrahim2012,

abstract = {In this paper, we show finite time blow-up of solutions of the p−wave
equation in ℝN, with critical Sobolev exponent. Our work
extends a result by Galaktionov and Pohozaev [4]},

author = {Ibrahim, S., Lyaghfouri, A.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {p−wave equation; Blow-up; critical Sobolev exponent; -wave equation},

language = {eng},

month = {2},

number = {2},

pages = {66-76},

publisher = {EDP Sciences},

title = {Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent},

url = {http://eudml.org/doc/222260},

volume = {7},

year = {2012},

}

TY - JOUR

AU - Ibrahim, S.

AU - Lyaghfouri, A.

TI - Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent

JO - Mathematical Modelling of Natural Phenomena

DA - 2012/2//

PB - EDP Sciences

VL - 7

IS - 2

SP - 66

EP - 76

AB - In this paper, we show finite time blow-up of solutions of the p−wave
equation in ℝN, with critical Sobolev exponent. Our work
extends a result by Galaktionov and Pohozaev [4]

LA - eng

KW - p−wave equation; Blow-up; critical Sobolev exponent; -wave equation

UR - http://eudml.org/doc/222260

ER -

## References

top- M. Agueh. A new ODE approach to sharp Sobolev inequalities. Nonlinear Analysis Research Trends. Nova Science Publishers, Inc. Editor : Inès N. Roux, pp. 1–13 (2008).
- T. Aubin. Problème isopérimétrique et espaces de Sobolev, J. Differential Geometry. 11, pp. 573–598 (1976). Zbl0371.46011
- C. Chen, H. Yao, L. Shao. Global Existence, Uniqueness, and Asymptotic Behavior of Solution for p-Laplacian Type Wave Equation. Journal of Inequalities and Applications Volume 2010, Article ID 216760, 15 pages. Zbl1211.35199
- V.A. Galaktionov, S.I. Pohozaev. Blow-up and critical exponents for nonlinear hyperbolic equations. Nonlinear Analysis 53, pp. 453–466 (2003). Zbl1012.35058
- G. Hongjun, Z. Hui. Global nonexistence of the solutions for a nonlinear wave equation with theq-Laplacian operator. J. Partial Diff. Eqs. 20 pp. 71–79(2007) . Zbl1142.35493
- S. Ibrahim, N. Masmoudi, K. Nakanishi. Scattering threshold for the focusing nonlinear Klein-Gordon equation. Analysis and PDE 4, No. 3, pp. 405–460, 2011. Zbl1270.35132
- C. E. Kenig, F. Merle. Global well-posedness, scattering and blow-up for the energy-critical, focusing, non-linear Schrödinger equation in the radial case. Invent. Math. 166, No. 3, pp. 645–675 (2006). Zbl1115.35125
- C. E. Kenig, F. Merle. Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation. Acta Math. 201, No. 2, pp. 147–212 (2008). Zbl1183.35202
- J. Shatah. Unstable ground state of nonlinear Klein-Gordon equations. Trans. Amer. Math. Soc. 290, No. 2, pp. 701–710 (1985). Zbl0617.35072
- G. Talenti. Best constants in Sobolev inequality. Ann. Mat. Pura Appl. 110, pp. 353–372 (1976). Zbl0353.46018
- Z. Wilstein. Global Well-Posedness for a Nonlinear Wave Equation withp-Laplacian Damping. Ph.D. thesis, University of Nebraska. Zbl1262.35151URIhttp://digitalcommons.unl.edu/mathstudent/24

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.