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

**[1]**A. Acker and B. Kawohl,*Remarks on quenching*, Nonlinear Anal. TMA**13**, 53-61 (1989) MR**973368****[2]**A. Acker and W. Walter,*The Quenching Problem for Nonlinear Parabolic Equations*, Springer Lecture Notes in Math., Vol. 564, 1976, pp. 1-12 MR**0604032****[3]**A. Acker and W. Walter,*On the global existence of solutions of parabolic differential equations with a singular nonlinear term*, Nonlinear Anal. TMA**2**, 499-505 (1978) MR**512487****[4]**K. Deng and H. A. Levine,*On the blow up of at quenching*, Proc. Amer. Math. Soc.**106**, 1049-1056 (1989) MR**969520****[5]**M. Fila,*Boundedness of global solutions of nonlinear diffusion equations*, Preprint 497, SFB 123, Heidelberg (1988) MR**1170469****[6]**M. Fila and B. Kawohl,*Asymptotic analysis of quenching problems*, Preprint 514, SFB 123, Heidelberg (1989), to appear in Rocky Mt. J. Math. MR**1180720****[7]**A. Friedman and B. McLeod,*Blow up of positive solutions of semilinear heat equations*, Indiana Univ. Math. J.**34**, 425-447 (1985) MR**783924****[8]**H. A. Levine,*Some nonexistence and instability theorems for solutions of formally parabolic equations of the form*, Arch. Rational Mech. Anal.**51**, 371-386 (1973) MR**0348216****[9]**H. A. Levine,*The quenching of solutions of linear parabolic and hyperbolic equations with nonlinear boundary conditions*, SIAM J. Math. Anal.**14**, 1139-1153 (1983) MR**718814****[10]**H. A. Levine,*The phenomenon of quenching: a survey*, Trends in the Theory and Practice of Nonlinear Analysis (V. Lakshmikantham, ed.), North Holland, 1985, pp. 275-286 MR**817500****[11]**H. A. Levine,*Quenching, nonquenching and beyond quenching for solutions of some parabolic equations*, Ann. Mat. Pura Appl., Ser. IV**CLV**, 243-260 (1989) MR**1042837****[12]**H. A. Levine and G. M. Lieberman,*Quenching of solutions of parabolic equations with nonlinear boundary conditions in several dimensions*, J. Reine Angew. Math.**345**, 23-38 (1983) MR**717884****[13]**H. A. Levine and J. T. Montgomery,*The quenching of solutions of some nonlinear parabolic equations*, SIAM J. Math. Anal.**11**, 842-847 (1980) MR**586912****[14]**W. M. Ni, P. E. Sacks, and J. Tavantzis,*On the asymptotic behaviour of solutions of certain quasilinear parabolic equations*, J. Differential Equations**54**, 97-120 (1984) MR**756548****[15]**H. Matano,*Existence of nontrivial unstable sets for equilibriums of strongly order preserving systems*, J. Fac. Sci. Tokyo**30**, 645-673 (1983) MR**731522**

Retrieve articles in *Quarterly of Applied Mathematics*
with MSC:
35B40,
35K57

Retrieve articles in all journals with MSC: 35B40, 35K57

Additional Information

DOI:
https://doi.org/10.1090/qam/1074968

Article copyright:
© Copyright 1990
American Mathematical Society