Geodesic
LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS
Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 569-575

Voir la notice de l'article provenant de la source Cambridge University Press

This paper deals with some non-linear initial-boundary value problems under homogeneous Neumann boundary conditions, in which the solutions may blow up in finite time. Using a first-order differential inequality technique, lower bounds for blow-up time are determined.
DOI : 10.1017/S0017089511000139
Mots-clés : 35K20, 35B45, 35B30 
ENACHE, CRISTIAN. LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS. Glasgow mathematical journal, Tome 53 (2011) no. 3, pp. 569-575. doi: 10.1017/S0017089511000139
@article{10_1017_S0017089511000139,
     author = {ENACHE, CRISTIAN},
     title = {LOWER {BOUNDS} {FOR} {BLOW-UP} {TIME} {IN} {SOME} {NON-LINEAR} {PARABOLIC} {PROBLEMS} {UNDER} {NEUMANN} {BOUNDARY} {CONDITIONS}},
     journal = {Glasgow mathematical journal},
     pages = {569--575},
     year = {2011},
     volume = {53},
     number = {3},
     doi = {10.1017/S0017089511000139},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000139/}
}
TY  - JOUR
AU  - ENACHE, CRISTIAN
TI  - LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS
JO  - Glasgow mathematical journal
PY  - 2011
SP  - 569
EP  - 575
VL  - 53
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000139/
DO  - 10.1017/S0017089511000139
ID  - 10_1017_S0017089511000139
ER  - 
%0 Journal Article
%A ENACHE, CRISTIAN
%T LOWER BOUNDS FOR BLOW-UP TIME IN SOME NON-LINEAR PARABOLIC PROBLEMS UNDER NEUMANN BOUNDARY CONDITIONS
%J Glasgow mathematical journal
%D 2011
%P 569-575
%V 53
%N 3
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000139/
%R 10.1017/S0017089511000139
%F 10_1017_S0017089511000139

[1] 1.Ball, J. M., Remarks on blow-up and non-existence theorems for nonlinear evolution equations, Q. J. Math. 28 (1977), 473–486. Google Scholar | DOI

[2] 2.Galaktionov, V. A. and Vazquez, J. L., The problem of blow-up in nonlinear parabolic equations, Discrete Cont. Dyn. Syst. 8 (2) (2002), 399–433. Google Scholar | DOI

[3] 3.Kielhöfer, H., Existenz und Regularität von Lösungen semilinearer parabolischer Anfangs-Randwertprobleme, Math. Z. 142 (1975), 131–160. Google Scholar | DOI

[4] 4.Levine, H. A., Nonexistence of global weak solutions to some properly and improperly posed problems of mathematical physics. The method of unbounded Fourier coefficients, Math. Ann. 214 (1975), 205–220. Google Scholar | DOI

[5] 5.Payne, L. E., Philippin, G. A. and Schaefer, P. W., Blow-up phenomena for some nonlinear parabolic problems, Nonlinear Anal. 69 (2008), 3495–3502. Google Scholar | DOI

[6] 6.Payne, L. E. and Schaefer, P. W., Lower bounds for blow-up time in parabolic problems under Neumann conditions, Appl. Anal. 85 (2006), 1301–1311. Google Scholar | DOI

[7] 7.Payne, L. E. and Schaefer, P. W., Lower bounds for blow-up time in parabolic problems under Dirichlet conditions, J. Math. Anal. Appl. 328 (2007), 1196–1205. Google Scholar | DOI

[8] 8.Payne, L. E. and Schaefer, P. W., Bounds for the blow-up time for the heat equation under nonlinear boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A. 139 (6) (2009), 1289–1296. Google Scholar | DOI

[9] 9.Payne, L. E. and Song, J. C., Lower bounds for blow-up time in a nonlinear parabolic problem, J. Math. Anal. Appl. 354 (2009), 294–396. Google Scholar | DOI

[10] 10.Protter, M. H. and Weinberger, H. F., Maximum principles in differential equations (Springer-Verlag, Berlin, 1975). Google Scholar

[11] 11.Quittner, R. and Souplet, P., Superlinear parabolic problems. Blow-up, global existence and steady states (Birkhauser, Basel, 2007). Google Scholar

[12] 12.Straughan, B., Explosive instabilities in mechanics (Springer-Verlag, Berlin, 1998). Google Scholar | DOI

Cité par Sources :