Comptes Rendus
no. 19-20
Partial differential equations
Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations
[Bornes inférieures du temps dʼexplosion des solutions dʼéquations paraboliques non linéaires sous forme de divergence dans des espaces de grande dimension]

Présenté par : the Editorial Board

Khadijeh Baghaei1 ; Mahmoud Hesaaraki2
1 Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
2 Department of Mathematics, Sharif University of Technology, Tehran, Iran
Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 731-735.
est référencé par Corrigendum to “Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations” [C. R. Acad. Sci. Paris, Ser. I 351 (19–20) (2013) 731–735]

Lʼarticle traite dʼun problème dʼexplosion des solutions dʼéquations paraboliques non linéaires sous forme de divergence, avec des conditions aux limites non linéaires. On obtient une estimation dʼune borne inférieure du temps dʼexplosion des solutions dans le cas dʼun domaine borné Ω⊆Rn, n⩾3.

This paper deals with the blow-up of solutions to some nonlinear divergence form parabolic equations with nonlinear boundary conditions. We obtain a lower bound for the blow-up time of solutions in a bounded domain Ω⊆Rn, n⩾3.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.09.024
Khadijeh Baghaei 1 ; Mahmoud Hesaaraki 2

1 Department of Mathematics, Iran University of Science and Technology, Tehran, Iran
2 Department of Mathematics, Sharif University of Technology, Tehran, Iran 
@article{CRMATH_2013__351_19-20_731_0,
     author = {Khadijeh Baghaei and Mahmoud Hesaaraki},
     title = {Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {731--735},
     publisher = {Elsevier},
     volume = {351},
     number = {19-20},
     year = {2013},
     doi = {10.1016/j.crma.2013.09.024},
     language = {en},
}
TY  - JOUR
AU  - Khadijeh Baghaei
AU  - Mahmoud Hesaaraki
TI  - Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations
JO  - Comptes Rendus. Mathématique
PY  - 2013
SP  - 731
EP  - 735
VL  - 351
IS  - 19-20
PB  - Elsevier
DO  - 10.1016/j.crma.2013.09.024
LA  - en
ID  - CRMATH_2013__351_19-20_731_0
ER  - 
%0 Journal Article
%A Khadijeh Baghaei
%A Mahmoud Hesaaraki
%T Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations
%J Comptes Rendus. Mathématique
%D 2013
%P 731-735
%V 351
%N 19-20
%I Elsevier
%R 10.1016/j.crma.2013.09.024
%G en
%F CRMATH_2013__351_19-20_731_0
Khadijeh Baghaei; Mahmoud Hesaaraki. Lower bounds for the blow-up time in the higher-dimensional nonlinear divergence form parabolic equations. Comptes Rendus. Mathématique, Volume 351 (2013) no. 19-20, pp. 731-735. doi : 10.1016/j.crma.2013.09.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2013.09.024/

[1] A. Bao; X. Song Bounds for the blow-up time of the solutions to quasi-linear parabolic problems, Z. Angew. Math. Phys. (2013) | DOI

[2] H. Brezis Analyse Fonctionnelle, Théorie et Applications, Masson, Paris, 1983

[3] H. Brezis Functional Analysis, Sobolev Spaces and Partial Differential Equations, Springer Science+Business Media, LLC, 2011

[4] C. Enache Lower bounds for blow-up time in some non-linear parabolic problems under Neumann boundary conditions, Glasg. Math. J., Volume 53 (2011), pp. 569-575

[5] F. Li; J. Li; Y. Wang Global existence and blow-up phenomena for nonlinear divergence form parabolic equations with inhomogeneous Neumann boundary conditions, J. Math. Anal. Appl., Volume 385 (2012), pp. 1005-1014

[6] L.E. Payne; G.A. Philippin; P.W. Schaefer Blow-up phenomena for some nonlinear parabolic problems, Nonlinear Anal., Volume 69 (2008), pp. 3495-3502

[7] L.E. Payne; G.A. Philippin; P.W. Schaefer Bounds for blow-up time in nonlinear parabolic problems, J. Math. Anal. Appl., Volume 338 (2008), pp. 438-447

[8] L.E. Payne; J.C. Song; P.W. Schaefer Lower bounds for blow-up time in a nonlinear parabolic problems, J. Math. Anal. Appl., Volume 354 (2009), pp. 394-396

[9] H.L. Zhang Blow-up solutions and global solutions for nonlinear parabolic problems, Nonlinear Anal. TMA, Volume 69 (2008), pp. 4567-4575

Cité par Sources :

Commentaires - Politique