Browse > Article
http://dx.doi.org/10.4134/JKMS.2007.44.4.779

BLOW-UP RATE ESTIMATES FOR A SYSTEM OF REACTION-DIFFUSION EQUATIONS WITH ABSORPTION  

Xiang, Zhaoyin (UNIVERSITY OF APPLIED MATHEMATICS UNIVERSITY OF ELECTRONIC SCIENCE AND TECHNOLOGY OF CHINA)
Chen, Qiong (DEPARTMENT OF MATHEMATICS SICHUAN UNIVERSITY)
Mu, Chunlai (DEPARTMENT OF MATHEMATICS SICHUAN UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.4, 2007 , pp. 779-786 More about this Journal
Abstract
In this note, we consider a system of two reaction-diffusion equations with absorption, under homogeneous Dirichlet boundary. Using scaling methods, we establish the blow-up rate estimates.
Keywords
reaction-diffusion systems; absorption; blowup rate estimates;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 1
연도 인용수 순위
1 B. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Commun. Paritial Differentail Equations 6 (1981), no. 8, 883-901   DOI   ScienceOn
2 J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Applied mathematical Sciences, 83, Springer-Verlag, New York, 1989
3 K. Deng, Blow-up rates for parabolic systems, Z. Angew. Math. Phys. 47 (1996), no. 1, 132-143   DOI
4 M. Escobedo and M. A. Herrero, Boundedness and blow up for a semilinear reaction-diffusion system, J. Differentail Equations 89 (1991), no. 1, 176-202   DOI
5 M. Fila and P. Quittner, The blow-up rate for a semilinear parabolic systems, J. Math. Anal. Appl. 238 (1999), no. 2, 468-476   DOI   ScienceOn
6 M. Fila and Ph. Souplet, The blow-up rate for semilinear parabolic problems on general domains, NoDEA Nonlinear Differentail Equations Appl. 8 (2001), no. 4, 473-480   DOI
7 N. Bedjaoui and Ph. Souplet,Critical blowup exponents for a system of reaction-diffusion equations with absorption, Z. Angew. Math. Phys. 53 (2002), no. 2, 197-210   DOI
8 M. Chlebik and M. Fila, From critical exponents to blow-up rates for parabolic problems, Rend. Mat. Appl. (7) 19 (1999), no. 4, 449-470
9 O. A. Lady-zenskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Providence, 1967
10 H. A. Levine, A Fujita type global existence - global nonexistence theorem for a weakly coupled system of reaction-diffusion equations, Z. Angew. Math. Phys. 42 (1991), no. 3, 408-430   DOI
11 Z. G. Lin, Blowup estimates for a mutualistic model in ecology, Electron. J. Qual. Theory Differ. Equ. (2002), no. 8, 1-14
12 S.-C. Fu and J.-S. Guo, Blow-up for a semilinear reaction-diffusion system coupled in both equations ans boundary conditions, J. Math. Anal. Appl. 296 (2002), no. 1, 458-475
13 B. Hu, Remarks on the blowup estimate for solutions of the heat equation with a non-linear boundary condition, Differential Integral Equations 9 (1996), no. 5, 891-901
14 B. Hu and H. M. Yin, The profile near blowup time for solution of the heat equation with a nonlinear boundary condition, Trans. Amer. Math. Soc. 346 (1994), no. 1, 117-135   DOI   ScienceOn
15 K. I. Kim and Z. G. Lin, Blowup estimates for a parabolic system in a three-species cooperating model, J. Math. Anal. Appl. 293 (2004), no. 2, 663-676   DOI   ScienceOn
16 F. Rothe, Global Solutions of Reaction-diffusion Systems, Lecture Notes in Mathematics, 1072, Springer-Verlag, Berlin, 1984
17 S. Snoussi and S. Tayachi, Global existence, asymptotic behavior and self-similar solutions for a class of semilinear parabolic systems, Nonlinear Anal. 48 (2002), no. 1, Ser. A : Theory Methods, 13-35   DOI   ScienceOn
18 P. Souplet and S. Tayachi, Optimal condition for non-simultaneous blow-up in a reaction-diffusion system, J. Math. Soc. Japan 56 (2004), no. 2, 571-584   DOI
19 M. X. Wang, Blow-up rate estimates for semilinear parabolic systems, J. Differentail Equations 170 (2001), no. 2, 317-324   DOI   ScienceOn
20 C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992