Single-point blow-up for a degenerate parabolic problem due to a concentrated nonlinear source

Authors:
C. Y. Chan and H. Y. Tian

Journal:
Quart. Appl. Math. **61** (2003), 363-385

MSC:
Primary 35K55; Secondary 35B45, 35K20, 35K65

DOI:
https://doi.org/10.1090/qam/1976376

MathSciNet review:
MR1976376

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a nonnegative real number, and be a positive real number. This article studies the following degenerate semilinear parabolic first initial-boundary value problem:

**[1]**C. Y. Chan and W. Y. Chan,*Existence of classical solutions for degenerate semilinear parabolic problems*, Appl. Math. Comput.**101**, 125-149 (1999) MR**1678117****[2]**C. Y. Chan and P. C. Kong,*Channel flow of a viscous fluid in the boundary layer*, Quart. Appl. Math.**55**, 51-56 (1997) MR**1433751****[3]**C. Y. Chan and H. T. Liu,*Global existence of solutions for degenerate semilinear parabolic problems*, Nonlinear Anal.**34**, 617-628 (1998) MR**1635771****[4]**M. S. Floater,*Blow-up at the boundary for degenerate semilinear parabolic equations*, Arch. Rat. Mech. Anal.**114**, 57-77 (1991) MR**1088277****[5]**A. Friedman,*Partial Differential Equations of Parabolic Type*, Prentice-Hall, Englewood Cliffs, NJ, 1964, pp. 39 and 49 MR**0181836****[6]**K. E. Gustafson,*Introduction to Partial Differential Equations and Hilbert Space Methods*, 2nd ed., John Wiley & Sons, New York, NY, 1987, p. 176 MR**881383****[7]**W. E. Olmstead and C. A. Roberts,*Explosion in a diffusive strip due to a concentrated nonlinear source*, Methods Appl. Anal.**1**, 435-445 (1994) MR**1317023****[8]**W. E. Olmstead and C. A. Roberts,*Explosion in a diffusive strip due to a source with local and nonlocal features*, Methods Appl. Anal.**3**, 345-357 (1996) MR**1421475****[9]**H. L. Royden,*Real Analysis*, 3rd ed., Macmillan Publishing Co., New York, NY, 1988, p. 87 MR**1013117****[10]**I. Stakgold,*Boundary Value Problems of Mathematical Physics*, vol. 1, Macmillan Co., New York, NY, 1967, pp. 38-39 MR**0205776****[11]**K. R. Stromberg,*An Introduction to Classical Real Analysis*, Wadsworth International Group, Belmont, CA, 1981, pp. 328, 352, and 380 MR**604364****[12]**G. N. Watson,*A Treatise on the Theory of Bessel Functions*, 2nd ed., Cambridge University Press, New York, NY, 1958, p. 506 MR**1349110**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
35K55,
35B45,
35K20,
35K65

Retrieve articles in all journals with MSC: 35K55, 35B45, 35K20, 35K65

Additional Information

DOI:
https://doi.org/10.1090/qam/1976376

Article copyright:
© Copyright 2003
American Mathematical Society