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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)
  • 발행 : 2007.07.30

초록

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.

키워드

참고문헌

  1. J. Bebernes and D. Eberly, Mathematical Problems from Combustion Theory, Applied mathematical Sciences, 83, Springer-Verlag, New York, 1989
  2. 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 https://doi.org/10.1007/s00033-002-8152-9
  3. 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
  4. K. Deng, Blow-up rates for parabolic systems, Z. Angew. Math. Phys. 47 (1996), no. 1, 132-143 https://doi.org/10.1007/BF00917578
  5. 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 https://doi.org/10.1016/0022-0396(91)90118-S
  6. M. Fila and P. Quittner, The blow-up rate for a semilinear parabolic systems, J. Math. Anal. Appl. 238 (1999), no. 2, 468-476 https://doi.org/10.1006/jmaa.1999.6525
  7. 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 https://doi.org/10.1007/PL00001459
  8. 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
  9. 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 https://doi.org/10.1080/03605308108820196
  10. 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
  11. 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 https://doi.org/10.2307/2154944
  12. 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 https://doi.org/10.1016/j.jmaa.2004.01.026
  13. O. A. Lady-zenskaja, V. A. Solonnikov, and N. N. Ural'ceva, Linear and quasilinear equations of parabolic type, Amer. Math. Soc. Providence, 1967
  14. 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 https://doi.org/10.1007/BF00945712
  15. Z. G. Lin, Blowup estimates for a mutualistic model in ecology, Electron. J. Qual. Theory Differ. Equ. (2002), no. 8, 1-14
  16. C. V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992
  17. F. Rothe, Global Solutions of Reaction-diffusion Systems, Lecture Notes in Mathematics, 1072, Springer-Verlag, Berlin, 1984
  18. 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 https://doi.org/10.1016/S0362-546X(00)00170-X
  19. 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 https://doi.org/10.2969/jmsj/1191418646
  20. M. X. Wang, Blow-up rate estimates for semilinear parabolic systems, J. Differentail Equations 170 (2001), no. 2, 317-324 https://doi.org/10.1006/jdeq.2000.3823

피인용 문헌

  1. Blow-up rates for degenerate parabolic equations coupled via equation and boundary vol.26, pp.3, 2011, https://doi.org/10.1080/14689367.2011.580333
  2. Blowup Analysis for a Nonlocal Diffusion Equation with Reaction and Absorption vol.2012, 2012, https://doi.org/10.1155/2012/648067
  3. Asymptotic analysis for reaction-diffusion equations with absorption vol.2012, pp.1, 2012, https://doi.org/10.1186/1687-2770-2012-84