L~1空间中L-R型迁移方程的解对边界参数的连续依赖性
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摘要
在L~1空间研究种群细胞增生中一类具扰动项的积分边界条件的迁移方程.证明了迁移算子是预解正算子,得到了微分算子的共轭算子,并证明其定义域的正锥在共轭空间的正锥中共尾,得到迁移算子的增长界等于其谱界.最后利用主算子对边界参数的连续依赖证明了迁移方程的解对边界参数连续依赖.
The objective of this paper is to research a transport equation of the integral boundary conditions with perturbationg term of cell population in L~1 space. We prove that transport operator is resolvent positive operator and obtain the adjoint operator of the differential operator and its domain. Then it was proved that the positive cone of domain of transport operator's adjoint operator is cofinal in positive cone of conjugate space. we obtain that the spectral bound of transport operator equals to its growth bound. Finally,With continuous dependence of resolvent's major operator to boundary parameter, we proved continuous dependence of transport equation's solution to boundary parameter.
The objective of this paper is to research a transport equation of the integral boundary conditions with perturbationg term of cell population in L~1 space. We prove that transport operator is resolvent positive operator and obtain the adjoint operator of the differential operator and its domain. Then it was proved that the positive cone of domain of transport operator's adjoint operator is cofinal in positive cone of conjugate space. we obtain that the spectral bound of transport operator equals to its growth bound. Finally,With continuous dependence of resolvent's major operator to boundary parameter, we proved continuous dependence of transport equation's solution to boundary parameter.
引文
[1]Lebowitz J L,Rubinow S I.A theory for the age generation time distribution of a microbial population[J].J Math Biol,1974,1:17-36.
[2]王胜华,程国飞.一类增生扩散型种群细胞中迁移方程的谱问题[J].数学物理学报,2013,33A(1):71-77.
[3]王胜华,贾善德,黄时祥.具扰动项的L-R型迁移算子的谱分析[J].系统科学与数学,2014,34(4):432-451.
[4]王胜华,贾善德,袁邓彬.种群细胞中一类迁移算子的谱分析[J].数学物理学报,2014,34A(6):1592-1598.
[5]贾善德,王胜华.具扰动项的L-R型迁移方程解的渐进性问题[J].应用泛函分析学报,2015,17(4):346-353.
[6]苑爽,王辉,任寒景,张欣.L~1空间中具有不完全反射边界条件的迁移方程的性质[J].数学的实践与认识,2015,45(16):166-171.
[7]Wolfgang Arendt.Resolvent Positive Operators[M].Proc.London Math.Soc,1987:321-349.
[8]Arams R A.Sobolev space[M].Pittsburgh:Academic Press,2003.
[2]王胜华,程国飞.一类增生扩散型种群细胞中迁移方程的谱问题[J].数学物理学报,2013,33A(1):71-77.
[3]王胜华,贾善德,黄时祥.具扰动项的L-R型迁移算子的谱分析[J].系统科学与数学,2014,34(4):432-451.
[4]王胜华,贾善德,袁邓彬.种群细胞中一类迁移算子的谱分析[J].数学物理学报,2014,34A(6):1592-1598.
[5]贾善德,王胜华.具扰动项的L-R型迁移方程解的渐进性问题[J].应用泛函分析学报,2015,17(4):346-353.
[6]苑爽,王辉,任寒景,张欣.L~1空间中具有不完全反射边界条件的迁移方程的性质[J].数学的实践与认识,2015,45(16):166-171.
[7]Wolfgang Arendt.Resolvent Positive Operators[M].Proc.London Math.Soc,1987:321-349.
[8]Arams R A.Sobolev space[M].Pittsburgh:Academic Press,2003.