一类非线性反应扩散方程组的定性分析Qualitative Analysis of a Quasilinear Reaction-diffusion System
张为元,李俊林
摘要(Abstract):
考虑一类非线性反应扩散方程组初边值问题解的整体存在性,爆破及稳定性等。通过构造上下解,利用比较原理得到了一些关于解的整体存在性和爆破的一些充分条件,同时给出了平凡定态解的局部稳定性。
关键词(KeyWords): 反应扩散方程组;上下解;整体存在性;爆破;稳定性
基金项目(Foundation): 山西省高校科技开发项目(200455,200513);; 咸阳师范学院科研项目(07XSYK284)
作者(Author): 张为元,李俊林
参考文献(References):
- [1]BEBERNES J,EBERLY D.Mathematical problems from combustion theory[M].New York:Spring-Ver-lag,1989.
- [2]GEL'FAND I M.Some problem in the theory of quasilinear equations[J].Amer.Math.Soc.Transl,1963,29(2):295-381.
- [3]JOSEPHD D,SPARROW E M.Nonlinear diffusion induced by nonlinear source[J].Quart,Appl.Math,1970,28:327-342.
- [4]KELLER HB,COHEN D S.Some positone problems suggested by nonlinear heat generation[J].J.Math.Mech,1967,16:1361-1376.
- [5]GU Y G,SUN W J.Nontrivial Equilibrium solutions for a semilinear reaction-diffusion system[J].Appl.Math.Mech,2004,25(12):1382-1389.
- [6]PAO C V.Nonlinear Prabolicand Elliptic Equations[M].NewYork:Plenum,1992.
- [7]ESCOBEDO M,HERRERO MA.A semilinear parabolic system in a bounded domain[J].Ann.Mat.Pura.Appl,1993,165:315-336.
- [8]WANG M X.Global existence and finite time blow up for reaction-diffusion system[J].Z.angew.Math.Phys,2000,51:160-167.
- [9]LIN Z G,XIE CH.一类半线性抛物系统正解的爆破速度[J].科学通报,1997,42(16):1717-1719.
- [10]LACEY AA.Mathematical analysis of thermal runaway for spatial inhomogeneous reactions[J].SIAM.J.Appl.Math,1983,43:1350-1366.
- [11]WANG M X.Qualitative analysis of a reaction-diffusion system[J].Appl.Math.Letters,2005,18:199-203.