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Online ISSN 1552-4485; Print ISSN 0033-569X
Is quenching in infinite time possible?
Authors:
Marek Fila and Bernhard Kawohl
Journal:
Quart. Appl. Math. 48 (1990), 531-534
MSC:
Primary 35B40; Secondary 35K57
DOI:
https://doi.org/10.1090/qam/1074968
MathSciNet review:
MR1074968
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
- Keng Deng and Howard A. Levine, On the blow up of $u_t$ at quenching, Proc. Amer. Math. Soc. 106 (1989), no. 4, 1049–1056. MR 969520, DOI https://doi.org/10.1090/S0002-9939-1989-0969520-0
- Marek Fila, Boundedness of global solutions of nonlinear diffusion equations, J. Differential Equations 98 (1992), no. 2, 226–240. MR 1170469, DOI https://doi.org/10.1016/0022-0396%2892%2990091-Z
- Marek Fila and Bernhard Kawohl, Asymptotic analysis of quenching problems, Rocky Mountain J. Math. 22 (1992), no. 2, 563–577. MR 1180720, DOI https://doi.org/10.1216/rmjm/1181072749
- Avner Friedman and Bryce McLeod, Blow-up of positive solutions of semilinear heat equations, Indiana Univ. Math. J. 34 (1985), no. 2, 425–447. MR 783924, DOI https://doi.org/10.1512/iumj.1985.34.34025
- Howard A. Levine, Some nonexistence and instability theorems for solutions of formally parabolic equations of the form $Pu_{t}=-Au+{\scr F}(u)$, Arch. Rational Mech. Anal. 51 (1973), 371–386. MR 348216, DOI https://doi.org/10.1007/BF00263041
- Howard A. Levine, The quenching of solutions of linear parabolic and hyperbolic equations with nonlinear boundary conditions, SIAM J. Math. Anal. 14 (1983), no. 6, 1139–1153. MR 718814, DOI https://doi.org/10.1137/0514088
- Howard A. Levine, The phenomenon of quenching: a survey, Trends in the theory and practice of nonlinear analysis (Arlington, Tex., 1984) North-Holland Math. Stud., vol. 110, North-Holland, Amsterdam, 1985, pp. 275–286. MR 817500, DOI https://doi.org/10.1016/S0304-0208%2808%2972720-8
- Howard A. Levine, Quenching, nonquenching, and beyond quenching for solution of some parabolic equations, Ann. Mat. Pura Appl. (4) 155 (1989), 243–260. MR 1042837, DOI https://doi.org/10.1007/BF01765943
- Howard A. Levine, The quenching of solutions of linear parabolic and hyperbolic equations with nonlinear boundary conditions, SIAM J. Math. Anal. 14 (1983), no. 6, 1139–1153. MR 718814, DOI https://doi.org/10.1137/0514088
- 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
- Wei-Ming Ni, Paul E. Sacks, and John Tavantzis, On the asymptotic behavior of solutions of certain quasilinear parabolic equations, J. Differential Equations 54 (1984), no. 1, 97–120. MR 756548, DOI https://doi.org/10.1016/0022-0396%2884%2990145-1
- Hiroshi Matano, Existence of nontrivial unstable sets for equilibriums of strongly order-preserving systems, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 (1984), no. 3, 645–673. MR 731522
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© Copyright 1990
American Mathematical Society