Quenching-rate estimate for a reaction diffusion equation with weakly singular reaction term

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

Volumn 11, Issue 4, 2004, Pages 469-480

  Salin, Timo ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

Blowup; Quenching; Quenching rate; Quenching set; Reaction diffusion equation

Indexed keywords

EID: 4544339794     PISSN: 12013390     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. A. Acker and B. Kawohl, Remarks on quenching, Nonlinear Analysis, TMA, 13, (1989) 53-61.
2. A. Acker and W. Walter, The quenching problem for nonlinear parabolic differential equations, in "Ordinary and Partial Differential Equations," (Eds. W.M. Everitt, B.D. Sleeman), Springer Lecture Notes in Math. 564, 1976, p. 1-12.
3. J. Bebernes and D. Eberly, A description of self-similar blow-up for dimensions n ≥ 3, Ann. Inst. Henri Poincaré, 5, (1988) 1-21.
4. t at quenching, Proc. Amer. Math. Soc, 106, (1989) 1049-1056.
5. M. Fila and J. Hulshof, A note on quenching rate, Proc. Amer. Math. Soc., 112, (1991) 473-477.
6. M. Fila, J. Hulshof and P. Quittner, The quenching problem on the N-dimensional ball, in "Nonlinear Diffusion Equations and their Equilibrium States, 3.," (Eds. N.G. Lloyd, W.M. Ni, J. Serrin, L.A. Peletier), Birkhäuser, Boston, 1992, p. 183-196.
7. M. Fila, H. A. Levine and J. L. Vazquez, Stabilization of solutions of weakly singular quenching problems, Proc. Amer. Math. Soc, 119, (1993) 555-559.
8. S. Filippas and J. Guo, Quenching profiles for one-dimensional heat equations, Quarterly of Applied Math., 51, (1993) 713-729.
9. p, Comm. Pure and Applied Mathematics, 45, (1992) 821-869.
10. B. Gidas, W-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68, (1979) 209-243.
11. Y. Giga and R. V. Kohn, Asymptotically self-similar blow-up of semi]inear heat equations, Comm. Pure Appl. Math., 38, (1985) 297-319.
12. Y. Giga and R. V. Kohn, Characterizing blow-up using similarity variables, Indiana University Mathematics Journal, 36, (1987) 1-40.
13. J. Guo, On the quenching behavior of the solution of a semilinear parabolic equation, J. Math. Anal. Appl., 151, (1990) 58-79.
14. n, Chinese J. Math., 19, (1991) 355-377.
15. J. Guo, On the quenching rate estimate, Quart. Appl. Math., 49, (1991) 747-752.
16. D. D. Joseph and T. S. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rat. Mech. Anal., 49, (1973) 241-269.
17. xx + 1/(1 - u), Publ. Res. Inst. Math. Sci., 10, (1975) 729-736.
18. B. Kawohl, Remarks on quenching (review), Documenta Mathematica, 1, (1996) 199-208.
19. H. Levine, Quenching, nonquenching and beyond quenching for solutions of some parabolic equations, Annali di Mat. Pura et Applicata, 155, (1990) 243-260.
20. H. Levine, Advances in quenching. in "Nonlinear Diffusion Equations and their Equilibrium States 3.," (Eds.: N. G. Lloyd, W. M. Ni, J. Serrin, L. A. Peletier), Birkhäuser, Boston, 1992, p. 319-346.
21. D. Phillips, Existence of solutions to a quenching problem, Appl. Anal., 24, (1987) 253-264.
22. T. Salin, On quenching with logarithmic singularity, Nonlinear Analysis TMA, 52, (2003) 261-289.
23. J. J. L Velazquez, Local behavior near blow-up points for semilinear parabolic equations, J. Differential Equations, 106, (1993) 384-415.
24. S. I. Yuen, Quenching rates for degenerate semilinear parabolic equations, Dynamic Systems and Applications, 6, (1997) 139-151.