Blow-up criteria for a parabolic problem due to a concentrated nonlinear source on a semi-infinite interval

Authors:
C. Y. Chan and T. Treeyaprasert

Journal:
Quart. Appl. Math. **70** (2012), 159-169

MSC (2010):
Primary 35K60, 35K57

DOI:
https://doi.org/10.1090/S0033-569X-2011-01255-0

Published electronically:
August 30, 2011

MathSciNet review:
2920621

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let , and be positive numbers, , , and . This article studies the first initial-boundary value problem,

**1.**C. Y. Chan and R. Boonklurb,*A blow-up criterion for a degenerate parabolic problem due to a concentrated nonlinear source*, Quart. Appl. Math. 65 (2007), 781-787. MR**2370360 (2008k:35231)****2.**C. Y. Chan and H. Y. Tian,*Single-point blow-up for a degenerate parabolic problem due to a concentrated nonlinear source*, Quart. Appl. Math. 61 (2003), 363-385. MR**1976376 (2004c:35173)****3.**C. Y. Chan and T. Treeyaprasert,*Blow-up due to a concentrated nonlinear source on a semi-infinite interval*, Proceedings of Dynamic Systems and Applications 5 (2008), 101-108. MR**2468124****4.**D. G. Duffy,*Green's Functions with Applications*, Chapman & Hall/CRC, Boca Raton, FL, 2001, p. 183. MR**1888091 (2003e:35005)****5.**A. Friedman,*Partial Differential Equations of Parabolic Type*, Prentice-Hall, Englewood Cliffs, NJ, 1964, pp. 34 and 49. MR**0181836 (31:6062)****6.**W. E. Olmstead and C. A. Roberts,*Explosion in a diffusive strip due to a concentrated nonlinear source*, Methods Appl. Anal. 1 (1994), 435-445. MR**1317023 (95k:35117)****7.**M. H. Protter and H. F. Weinberger,*Maximum Principles in Differential Equations,*Prentice-Hall, Englewood Cliffs, NJ, 1967, pp. 183-185. MR**0219861 (36:2935)**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC (2010):
35K60,
35K57

Retrieve articles in all journals with MSC (2010): 35K60, 35K57

Additional Information

**C. Y. Chan**

Affiliation:
Department of Mathematics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504-1010

Email:
chan@louisiana.edu

**T. Treeyaprasert**

Affiliation:
Department of Mathematics and Statistics, Thammasat University Rangsit Center, Pathumthani, 12121 Thailand

Email:
tawikan@tu.ac.th

DOI:
https://doi.org/10.1090/S0033-569X-2011-01255-0

Keywords:
Semilinear parabolic first initial-boundary value problem,
semi-infinite interval,
concentrated nonlinear source,
single blow-up point,
critical position,
global existence

Received by editor(s):
August 26, 2010

Published electronically:
August 30, 2011

Article copyright:
© Copyright 2011
Brown University