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 Free Access
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Additional Information
Abstract: This article studies a semilinear parabolic first initial-boundary value problem with a concentrated nonlinear source in an $N$-dimensional infinite strip. Criteria for the solution to quench are given.
References
- 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, DOI https://doi.org/10.1090/qam/2086046
- 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, DOI https://doi.org/10.1137/0520039
- C. Y. Chan and P. Tragoonsirisak, A multi-dimensional quenching problem due to a concentrated nonlinear source in $\Bbb R^N$, Nonlinear Anal. 69 (2008), no. 5-6, 1494–1514. MR 2424525, DOI https://doi.org/10.1016/j.na.2007.07.001
- C. Y. Chan and P. Tragoonsirisak, A multi-dimensional blow-up problem due to a concentrated nonlinear source in $\Bbb R^N$, Quart. Appl. Math. 69 (2011), no. 2, 317–330. MR 2814530, DOI https://doi.org/10.1090/S0033-569X-2011-01219-3
- 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
- Karl R. Stromberg, Introduction to classical real analysis, Wadsworth International, Belmont, Calif., 1981. Wadsworth International Mathematics Series. MR 604364
- W. R. Wade, An Introduction to Analysis, 2nd ed., Prentice-Hall, Upper Saddle River, NJ, 2000, pp. 190-191.
References
- 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)
- 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)
- C. Y. Chan and P. Tragoonsirisak, A multi-dimensional quenching problem due to a concentrated nonlinear source in $\mathbb {R}^{N}$, Nonlinear Anal. 69 (2008), 1494-1514. MR 2424525 (2009g:35128)
- C. Y. Chan and P. Tragoonsirisak, A multi-dimensional blow-up problem due to a concentrated nonlinear source in $\mathbb {R}^{N}$, Quart. Appl. Math. 69 (2011), 317-330. MR 2814530 (2012e:35130)
- 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
- K. R. Stromberg, An Introduction to Classical Real Analysis, Wadsworth, Belmont, CA, 1981, pp. 266-268, and 518. MR 604364 (82c:26002)
- 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
MR Author ID:
203257
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
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
