Critical lengths for semilinear singular parabolic mixed boundary value problems
Authors:
C. Y. Chan and Shannon S. Cobb
Journal:
Quart. Appl. Math. 49 (1991), 497-506
MSC:
Primary 35B05; Secondary 35B50, 35K60
DOI:
https://doi.org/10.1090/qam/1121682
MathSciNet review:
MR1121682
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- Andrew F. Acker and Bernhard Kawohl, Remarks on quenching, Nonlinear Anal. 13 (1989), no. 1, 53–61. MR 973368, DOI https://doi.org/10.1016/0362-546X%2889%2990034-5
- Andrew Acker and Wolfgang Walter, The quenching problem for nonlinear parabolic differential equations, Ordinary and partial differential equations (Proc. Fourth Conf., Univ. Dundee, Dundee, 1976) Springer, Berlin, 1976, pp. 1–12. Lecture Notes in Math., Vol. 564. MR 0604032
- Andrew Acker and Wolfgang Walter, On the global existence of solutions of parabolic differential equations with a singular nonlinear term, Nonlinear Anal. 2 (1978), no. 4, 499–504. MR 512487, DOI https://doi.org/10.1016/0362-546X%2878%2990057-3
- C. Y. Chan and C. S. Chen, A numerical method for semilinear singular parabolic quenching problems, Quart. Appl. Math. 47 (1989), no. 1, 45–57. MR 987894, DOI https://doi.org/10.1090/S0033-569X-1989-0987894-4
- C. Y. Chan and C. S. Chen, Critical lengths for global existence of solutions for coupled semilinear singular parabolic problems, Quart. Appl. Math. 47 (1989), no. 4, 661–671. MR 1031683, DOI https://doi.org/10.1090/qam/1031683
- 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 Man Kam Kwong, Existence results of steady-states of semilinear reaction-diffusion equations and their applications, J. Differential Equations 77 (1989), no. 2, 304–321. MR 983297, DOI https://doi.org/10.1016/0022-0396%2889%2990146-0
- Avner Friedman, Partial differential equations of parabolic type, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0181836
- Hideo Kawarada, On solutions of initial-boundary problem for $u_{t}=u_{xx}+1/(1-u)$, Publ. Res. Inst. Math. Sci. 10 (1974/75), no. 3, 729–736. MR 0385328, DOI https://doi.org/10.2977/prims/1195191889
- Howard A. Levine and John T. Montgomery, The quenching of solutions of some nonlinear parabolic equations, SIAM J. Math. Anal. 11 (1980), no. 5, 842–847. MR 586912, DOI https://doi.org/10.1137/0511075
G. N. Polozhiy, Equations of Mathematical Physics, Hayden, New York, 1967, p. 413
- Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984. Corrected reprint of the 1967 original. MR 762825
- H. L. Royden, Real analysis, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1963. MR 0151555
A. Acker and B. Kawohl, Remarks on quenching, Nonlinear Anal. 13, 53–61 (1989)
A. Acker and W. Walter, The quenching problem for nonlinear parabolic differential equations, Lecture Notes in Math., Vol. 564, Springer-Verlag, New York, 1976, pp. 1–12
A. Acker and W. Walter, On the global existence of solutions of parabolic differential equations with a singular nonlinear term, Nonlinear Anal. 2, 499–505 (1978)
C. Y. Chan and C. S. Chen, A numerical method for semilinear singular parabolic quenching problems, Quart. Appl. Math. 47, 45–57 (1989)
C. Y. Chan and C. S. Chen, Critical lengths for global existence of solutions for coupled semilinear singular parabolic problems, Quart. Appl. Math. 47, 661–671 (1989)
C. Y. Chan and H. G. Kaper, Quenching for semilinear singular parabolic problems, SIAM J. Math. Anal. 20, 558–566 (1989)
C. Y. Chan and M. K. Kwong, Existence results of steady-states of semilinear reaction-diffusion equations and their applications, J. Differential Equations 77, 304–321 (1989)
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice-Hall, Englewood Cliffs, NJ, 1964, pp. 26–27, 82–84 and 155
H. Kawarada, On solutions of initial-boundary problem for ${u_t} = {u_{xx}} + {\left ( {1 - u} \right )^{ - 1}}$, Publ. Res. Inst. Math. Sci. 10, 729–736 (1975)
H. A. Levine and J. T. Montgomery, The quenching of solutions of some nonlinear parabolic equations, SIAM J. Math. Anal. 11, 842–847 (1980)
G. N. Polozhiy, Equations of Mathematical Physics, Hayden, New York, 1967, p. 413
M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984, pp. 168–172 and 175
H. L. Royden, Real Analysis, 2nd ed., Macmillan, New York, 1968, p. 84
Similar Articles
Retrieve articles in Quarterly of Applied Mathematics
with MSC:
35B05,
35B50,
35K60
Retrieve articles in all journals
with MSC:
35B05,
35B50,
35K60
Additional Information
Article copyright:
© Copyright 1991
American Mathematical Society