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

Published electronically:
August 30, 2011

MathSciNet review:
2920621

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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), no. 4, 781–787. MR**2370360**, 10.1090/S0033-569X-07-01082-9**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), no. 2, 363–385. MR**1976376****3.**C. Y. Chan and T. Treeyaprasert,*Blow-up due to a concentrated nonlinear source on a semi-infinite interval*, Dynamic systems and applications. Vol. 5, Dynamic, Atlanta, GA, 2008, pp. 101–108. MR**2468124****4.**Dean G. Duffy,*Green’s functions with applications*, Studies in Advanced Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2001. MR**1888091****5.**Avner Friedman,*Partial differential equations of parabolic type*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR**0181836****6.**W. E. Olmstead and Catherine A. Roberts,*Explosion in a diffusive strip due to a concentrated nonlinear source*, Methods Appl. Anal.**1**(1994), no. 4, 434–445. MR**1317023**, 10.4310/MAA.1994.v1.n4.a5**7.**Murray H. Protter and Hans F. Weinberger,*Maximum principles in differential equations*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1967. MR**0219861**

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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:
http://dx.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