On quenching with logarithmic singularity

Nonlinear Analysis, Theory, Methods and Applications

Volumn 52, Issue 1, 2003, Pages 261-289

  Salin, Timo ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Blow up; Quenching; Quenching rate; Quenching set; Reaction diffusion equation

Indexed keywords

ASYMPTOTIC STABILITY; DIFFUSION; INTEGRATION; PROBLEM SOLVING; QUENCHING;

NONLINEAR DIFFUSION PROBLEM;

NONLINEAR EQUATIONS;

EID: 0037209546     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(02)00110-4     Document Type: Article

References (27)

1. Acker A., Kawohl B. Remarks on quenching. Nonlinear Analysis TMA. 13:1989;53-61.
2. Acker A., Walter W. The quenching problem for nonlinear parabolic differential equations. Everitt W.M., Sleeman B.D. Ordinary and Partial Differential Equations. Lecture Notes in Mathematics. Vol. 564:1976;1-12 Dundee, Springer, Berlin.
3. Angenent S. The zero set of solutions of a parabolic equation. J. Reine Angew. Math. 390:1988;79-96.
4. Bebernes J., Eberly D. A description of self-similar blow-up for dimensions. n≥ 3 Ann. Inst. Henri Poincaré 5:1988;1-21.
5. t at quenching Proc. Amer. Math. Soc. 106:1989;1049-1056.
6. Fila M., Hulshof J. A note on quenching rate. Proc. Amer. Math. Soc. 112:1991;473-477.
7. Fila M., Hulshof J., Quittner P. The quenching problem on the. N -dimensional ball Lloyd N.G., Ni W.M., Serrin J., Peletier L.A. Nonlinear Diffusion Equations and their Equlibrium States 3. 1992;183-196 Birkhäuser, Boston.
8. Fila M., Levine H.A., Vazquez J.L. Stabilization of solutions of weakly singular quenching problems. Proc. Amer. Math. Soc. 119:1993;555-559.
9. Filippas S., Guo J. Quenching profiles for one-dimensional heat equations. Quart. Appl. Math. 51:1993;713-729.
10. p Comm. Pure Appl. Math. 45:1992;821-869.
11. Friedman A. Partial Differential Equations of Parabolic Type. 1964;Prentice-Hall, Englewood Cliffs, NJ.
12. Giga Y., Kohn R.V. Asymptotically self-similar blow-up of semilinear heat equations. Comm. Pure Appl. Math. 38:1985;297-319.
13. Giga Y., Kohn R. Characterizing blow-up using similarity variables. Indiana Univ. Math. J. 36:1987;1-40.
14. Guo J. On the quenching behavior of the solution of a semilinear parabolic equation. J. Math. Anal. Appl. 151:1990;58-79.
15. Guo J. On the quenching rate estimate. Quart. Appl. Math. 49:1991;747-752.
16. xx+1/(1-u) Publ. Res. Inst. Math. Sci. 10:1975;729-736.
17. Kawohl B. Remarks on quenching (review) Documenta Math. 1:1996;199-208.
18. Kawohl B., Peletier L. Observations on blow-up and dead cores for nonlinear parabolic equations. Math. Zeit. 202:1989;207-217.
19. Levine H. Quenching, nonquenching and beyond quenching for solutions of some parabolic equations. Ann. di Mat. Pura Appl. 155:1990;243-260.
20. Levine H., Montgomery J. The quenching of solutions of some nonlinear parabolic equations. SIAM J. Math. Anal. 11:1980;842-847.
21. Levine H. The role of critical exponents in blowup theorems. SIAM Rev. 32:1990;262-288.
22. H. Levine, Advances in quenching, in: N.G. Lloyd, W.M. Ni, J. Serrin, L.A. Peletier (Eds.), Nonlinear Diffusion Equations and their Equlibrium States, Birkhäuser, Boston, 1192, pp. 319-346.
23. Phillips D. Existence of solutions to a quenching problem. Appl. Anal. 24:1987;253-264.
24. Souplet P. Finite time blow-up for a nonlinear parabolic equation with a gradient term and applications. Math. Meth. Appl. Sci. 19:1996;1317-1333.
25. Souplet P., Tayachi S., Weissler F. Exact self-similar blow-up of solutions of a semilinear parabolic equation with a nonlinear gradient term. Indiana Univ. Math. J. 45:1996;655-682.
26. Sperp R. Maximum Principles and Their Applications. 1981;Academic Press, New York.
27. L Velazquez J.J. Local behavior near blow-up points for semilinear parabolic equations. J. Differential Equations. 106:1993;384-415.