一类带有加权非局部源和吸收项的抛物方程组解的爆破
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摘要
处理了一类更复杂的抛物方程组解的整体存在性和爆破性,方程组带有内吸收且非局部源项的系数是函数,这跟常系数的情形有本质的区别.在一定条件下,分别证明了解的全局爆破和爆破速率.
This paper deals with the global existence and blow up properties of solutions for a more com- plicate parabolic equations with weighted nonlocal sources and absorptions.This is essentially different from the situation of constant coefficients.Under certain conditions,the global blow up of solutions and the rates of blow up are shown respectively.
This paper deals with the global existence and blow up properties of solutions for a more com- plicate parabolic equations with weighted nonlocal sources and absorptions.This is essentially different from the situation of constant coefficients.Under certain conditions,the global blow up of solutions and the rates of blow up are shown respectively.
引文
[1]Donald S.Cohen,James D.Murray.A generalized diffusion model for growth and dispersal in a population[J].Journal of Mathematical Biology,1981,12(2):237-249.
[2]Purter J,Grinfeld M.Local vs.non-local interactions in population dynamics[J].Journal of Mathematical Biology,1989,27(1):65-80.
[3]Chen Youpeng.Blow-up for a System of Heat Equations with Nonlocal Sources and Absorptions[J].Computers and Mathematics with Applications,2004,48(3):361-372.
[4]Qiao Lan,Zheng Sining.Asymptotic analysis of a coupled nonlinear parabolic system[J].Frontiers of Mathematics in China,2008,3(1):87-99.
[5]Jiang Liangjun,Xu Yongping.Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source[J].Journal of Mathematical Analysis and Applications,2009,365(1):50-59.
[6]Liu Qilin,Li Yuxiang,Gao Hongjun.Uniform blow-up rate for diffusion equations with nonlocal nonlinear source[J].Nonlinear Analysis,2007,67(6):1947-1957.
[7]Deng Weibing,Xie Chunhong.Blow-up and global existence for a nonlocal degenerate parabolic[J].Journal of Mathematical Analysis and Applications,2003,277(1):199-217.
[8]Souplet P.Blow-up in nonlocal reaction-diffusion equations[J].SIAM Journal of Mathematical Analysis,1998,29(6):1301-1334.
[9]Souplet P.Uniform blow-up profile and boundary behavior for diffusion equations with nonlocal nonlinear source[J].Journal of Differential Equations,1999,153(2):374-406.
[10]Hu Bei,Yin Hongming.The profile near blow up time for the solution of the heat equation with a nonlinear boundary condition[J].Transactions of the American Mathematical Society,1994,346(1):117-135.
[11]孔令花,赵立中,郑斯宁.具有内吸收和耦合局部化源的抛物组的渐近分析[J].数学物理学报,2010,30A(1):267-277.
[12]李娟,崔泽建.带非局部源和吸收项的退化奇异抛物方程的爆破[J].四川大学学报,2008,45(1):35-40.
[13l徐昌贵,林红霞.带非局部源的退化奇异半线性抛物方程组爆破解的渐进行为[J].西南民族大学学报,2007,33(2):250-255.
[14]高海燕,伏升茂.强耦合竞争-竞争-互惠模型古典解的整体存在性[J].生物数学学报,2007,22(4):645-651.
[15]安海龙,杨芳,李艳玲.带饱和项的互惠交错扩散模型整体解的存在性和稳定性[J].生物数学学报,2009,24(4):649-656.
[2]Purter J,Grinfeld M.Local vs.non-local interactions in population dynamics[J].Journal of Mathematical Biology,1989,27(1):65-80.
[3]Chen Youpeng.Blow-up for a System of Heat Equations with Nonlocal Sources and Absorptions[J].Computers and Mathematics with Applications,2004,48(3):361-372.
[4]Qiao Lan,Zheng Sining.Asymptotic analysis of a coupled nonlinear parabolic system[J].Frontiers of Mathematics in China,2008,3(1):87-99.
[5]Jiang Liangjun,Xu Yongping.Uniform blow-up rate for parabolic equations with a weighted nonlocal nonlinear source[J].Journal of Mathematical Analysis and Applications,2009,365(1):50-59.
[6]Liu Qilin,Li Yuxiang,Gao Hongjun.Uniform blow-up rate for diffusion equations with nonlocal nonlinear source[J].Nonlinear Analysis,2007,67(6):1947-1957.
[7]Deng Weibing,Xie Chunhong.Blow-up and global existence for a nonlocal degenerate parabolic[J].Journal of Mathematical Analysis and Applications,2003,277(1):199-217.
[8]Souplet P.Blow-up in nonlocal reaction-diffusion equations[J].SIAM Journal of Mathematical Analysis,1998,29(6):1301-1334.
[9]Souplet P.Uniform blow-up profile and boundary behavior for diffusion equations with nonlocal nonlinear source[J].Journal of Differential Equations,1999,153(2):374-406.
[10]Hu Bei,Yin Hongming.The profile near blow up time for the solution of the heat equation with a nonlinear boundary condition[J].Transactions of the American Mathematical Society,1994,346(1):117-135.
[11]孔令花,赵立中,郑斯宁.具有内吸收和耦合局部化源的抛物组的渐近分析[J].数学物理学报,2010,30A(1):267-277.
[12]李娟,崔泽建.带非局部源和吸收项的退化奇异抛物方程的爆破[J].四川大学学报,2008,45(1):35-40.
[13l徐昌贵,林红霞.带非局部源的退化奇异半线性抛物方程组爆破解的渐进行为[J].西南民族大学学报,2007,33(2):250-255.
[14]高海燕,伏升茂.强耦合竞争-竞争-互惠模型古典解的整体存在性[J].生物数学学报,2007,22(4):645-651.
[15]安海龙,杨芳,李艳玲.带饱和项的互惠交错扩散模型整体解的存在性和稳定性[J].生物数学学报,2009,24(4):649-656.