Geodesic
Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent
S. Ibrahim1 ; A. Lyaghfouri2
1 Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
2 Fields Institute, Toronto, ON, Canada
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 66-76.

Voir la notice de l'article provenant de la source EDP Sciences

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]
DOI : 10.1051/mmnp/20127206

S. Ibrahim 1 ; A. Lyaghfouri 2

1 Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
2 Fields Institute, Toronto, ON, Canada 
@article{MMNP_2012_7_2_a5,
     author = {S. Ibrahim and A. Lyaghfouri},
     title = {Blow-up {Solutions} of {Quasilinear} {Hyperbolic} {Equations} {With} {Critical} {Sobolev} {Exponent}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {66--76},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2012},
     doi = {10.1051/mmnp/20127206},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127206/}
}
TY  - JOUR
AU  - S. Ibrahim
AU  - A. Lyaghfouri
TI  - Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent
JO  - Mathematical modelling of natural phenomena
PY  - 2012
SP  - 66
EP  - 76
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127206/
DO  - 10.1051/mmnp/20127206
LA  - en
ID  - MMNP_2012_7_2_a5
ER  - 
%0 Journal Article
%A S. Ibrahim
%A A. Lyaghfouri
%T Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent
%J Mathematical modelling of natural phenomena
%D 2012
%P 66-76
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127206/
%R 10.1051/mmnp/20127206
%G en
%F MMNP_2012_7_2_a5
S. Ibrahim; A. Lyaghfouri. Blow-up Solutions of Quasilinear Hyperbolic Equations With Critical Sobolev Exponent. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 2, pp. 66-76. doi : 10.1051/mmnp/20127206. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127206/

[1] 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).

[2] T. Aubin. Problème isopérimétrique et espaces de Sobolev, J. Differential Geometry. 11, pp. 573–598 (1976).

[3] 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.

[4] V.A. Galaktionov, S.I. Pohozaev. Blow-up and critical exponents for nonlinear hyperbolic equations. Nonlinear Analysis 53, pp. 453–466 (2003).

[5] G. Hongjun, Z. Hui. Global nonexistence of the solutions for a nonlinear wave equation with the q-Laplacian operator. J. Partial Diff. Eqs. 20 pp. 71–79(2007) .

[6] 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.

[7] 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).

[8] 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).

[9] J. Shatah. Unstable ground state of nonlinear Klein-Gordon equations. Trans. Amer. Math. Soc. 290, No. 2, pp. 701–710 (1985).

[10] G. Talenti. Best constants in Sobolev inequality. Ann. Mat. Pura Appl. 110, pp. 353–372 (1976).

[11] Z. Wilstein. Global Well-Posedness for a Nonlinear Wave Equation with p-Laplacian Damping. Ph.D. thesis, University of Nebraska. http://digitalcommons.unl.edu/mathstudent/24

Cité par Sources :