具有局部化源项的扩散系统解的整体有界与爆破准则(英文)
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摘要
文章研究一类同时具有正的Dirichlet边界条件与局部化源项的幂指数形式的扩散系统,得到系统正解的爆破准则与整体有界的条件.这些结果不仅扩充了已有的结论[5-6],而且证明了系统的边界值ε0在决定问题解的爆破与否中起着关键的作用.
This paper considers a localized diffusion system coupled via nonlinear reaction terms of power type with positive Dirichlet boundary value.The blow-up criteria and global boundedness conditions of positive solutions are determined.These results not only extend those by ZHANG [5] and LING [6] , but also show the positive Dirichlet boundary valueε 0 plays an important role in the case of blow-up.
This paper considers a localized diffusion system coupled via nonlinear reaction terms of power type with positive Dirichlet boundary value.The blow-up criteria and global boundedness conditions of positive solutions are determined.These results not only extend those by ZHANG [5] and LING [6] , but also show the positive Dirichlet boundary valueε 0 plays an important role in the case of blow-up.
引文
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[4]ZHENG Sining.Global existence global non-existence of solutions to a reaction-diffusion system[J].Non-linear Anal.,2000,39:327-340.
[5]ZHANG Rui,YANG Zuodong.Uniform blow-up rates and asymptotic estimates of solutions for diffusion systems with weighted localized sources[J].J.Appl.Math.Comput.,2010,32:429-441.
[6]LING Zhengqiu,WANG Zejia.Simultaneous and non-simultaneous blow-up criteria of solutions for a dif-fusion system with weighted localized sources[J].J.Appl.Math.Comput.,2012,40:183-194.
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[8]Courant R,Hilbert D.Methods of Mathmatical Physics[M].New York:Interscience Publishers Inc.,1962.
[2]Escobedo M,Levine H A.Critical blow-up and global existence numbers for a weakly coupled system of reaction-diffusion equations[J].Arch.Rational Mech.Anal.,1995,129:47-100.
[3]ZHENG Sining.Global boundedness of solutions to a reaction-diffusion system[J].Math.Meth.Appl.Sci.,1999,22:43-54.
[4]ZHENG Sining.Global existence global non-existence of solutions to a reaction-diffusion system[J].Non-linear Anal.,2000,39:327-340.
[5]ZHANG Rui,YANG Zuodong.Uniform blow-up rates and asymptotic estimates of solutions for diffusion systems with weighted localized sources[J].J.Appl.Math.Comput.,2010,32:429-441.
[6]LING Zhengqiu,WANG Zejia.Simultaneous and non-simultaneous blow-up criteria of solutions for a dif-fusion system with weighted localized sources[J].J.Appl.Math.Comput.,2012,40:183-194.
[7]Ladyzhenskaja O A,Solonikov V A,Uraltzeva N N.Linear and quasilinear equations of parabolic type[G]//Transl.Math.Mono.,23,Providence RI:AMS,1968.
[8]Courant R,Hilbert D.Methods of Mathmatical Physics[M].New York:Interscience Publishers Inc.,1962.