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

Published electronically:
May 20, 2013

MathSciNet review:
3112827

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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), no. 3, 553–568. MR**2086046****2.**C. Y. Chan and Hans G. Kaper,*Quenching for semilinear singular parabolic problems*, SIAM J. Math. Anal.**20**(1989), no. 3, 558–566. MR**990863**, 10.1137/0520039**3.**C. Y. Chan and P. Tragoonsirisak,*A multi-dimensional quenching problem due to a concentrated nonlinear source in ℝ^{ℕ}*, Nonlinear Anal.**69**(2008), no. 5-6, 1494–1514. MR**2424525**, 10.1016/j.na.2007.07.001**4.**C. Y. Chan and P. Tragoonsirisak,*A multi-dimensional blow-up problem due to a concentrated nonlinear source in ℝ^{ℕ}*, Quart. Appl. Math.**69**(2011), no. 2, 317–330. MR**2814530**, 10.1090/S0033-569X-2011-01219-3**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), no. 4, 505–517. MR**2884683****6.**Karl R. Stromberg,*Introduction to classical real analysis*, Wadsworth International, Belmont, Calif., 1981. Wadsworth International Mathematics Series. MR**604364****7.**W. R. Wade,*An Introduction to Analysis*, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 2000, pp. 190-191.

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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:
http://dx.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