Quenching criteria for a parabolic problem due to a concentrated nonlinear source in an infinite strip

Authors:
C. Y. Chan and P. Tragoonsirisak

Journal:
Quart. Appl. Math. **71** (2013), 541-548

MSC (2010):
Primary 35K60, 35B35, 35K55, 35K57

DOI:
https://doi.org/10.1090/S0033-569X-2013-01315-3

Published electronically:
May 20, 2013

MathSciNet review:
3112827

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an -dimensional infinite strip. Criteria for the solution to quench are given.

**1.**C. Y. Chan and X. O. Jiang,*Quenching for a degenerate parabolic problem due to a concentrated nonlinear source*, Quart. Appl. Math.**62**(2004), 553-568. MR**2086046 (2005e:35139)****2.**C. Y. Chan and H. G. Kaper,*Quenching for semilinear singular parabolic problems*, SIAM J. Math. Anal.**20**(1989), 558-566. MR**990863 (91e:35030)****3.**C. Y. Chan and P. Tragoonsirisak,*A multi-dimensional quenching problem due to a concentrated nonlinear source in*, Nonlinear Anal.**69**(2008), 1494-1514. MR**2424525 (2009g:35128)****4.**C. Y. Chan and P. Tragoonsirisak,*A multi-dimensional blow-up problem due to a concentrated nonlinear source in*, Quart. Appl. Math.**69**(2011), 317-330. MR**2814530 (2012e:35130)****5.**C. Y. Chan and P. Tragoonsirisak,*A quenching problem due to a concentrated nonlinear source in an infinite strip*, Dynam. Systems Appl.**20**(2011), 505-518. MR**2884683****6.**K. R. Stromberg,*An Introduction to Classical Real Analysis*, Wadsworth, Belmont, CA, 1981, pp. 266-268, and 518. MR**604364 (82c:26002)****7.**W. R. Wade,*An Introduction to Analysis*, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 2000, pp. 190-191.

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC (2010):
35K60,
35B35,
35K55,
35K57

Retrieve articles in all journals with MSC (2010): 35K60, 35B35, 35K55, 35K57

Additional Information

**C. Y. Chan**

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

Email:
chan@louisiana.edu

**P. Tragoonsirisak**

Affiliation:
Department of Mathematics and Computer Science, Fort Valley State University, Fort Valley, Georgia 31030

Email:
tragoonsirisakp@fvsu.edu

DOI:
https://doi.org/10.1090/S0033-569X-2013-01315-3

Keywords:
Quenching criteria,
concentrated nonlinear source,
infinite strip.

Received by editor(s):
September 24, 2011

Published electronically:
May 20, 2013

Article copyright:
© Copyright 2013
Brown University