数学物理学报
數學物理學報
수학물이학보
ACTA MATHEMATICA SCIENTIA
2010年
2期
440-448
,共9页
反应扩散系统%双稳波前解%全局渐近稳定性
反應擴散繫統%雙穩波前解%全跼漸近穩定性
반응확산계통%쌍은파전해%전국점근은정성
Reaction-diffusion system%Bistable traveling wave front%Global asymptotic sta-bility
该文研究一类拟单调反应扩散系统的古典解的渐近行为.在双稳的假定下,利用上,下解方法和单调半流的收敛性结果,证明了当系统的初值在±∞处的极限分别'呔于"和"小于"其中间平衡点时,初值问题的解收敛于一个连接两个稳定平衡点的波前解.最后,将结果应用到一个传染病模型.
該文研究一類擬單調反應擴散繫統的古典解的漸近行為.在雙穩的假定下,利用上,下解方法和單調半流的收斂性結果,證明瞭噹繫統的初值在±∞處的極限分彆'呔于"和"小于"其中間平衡點時,初值問題的解收斂于一箇連接兩箇穩定平衡點的波前解.最後,將結果應用到一箇傳染病模型.
해문연구일류의단조반응확산계통적고전해적점근행위.재쌍은적가정하,이용상,하해방법화단조반류적수렴성결과,증명료당계통적초치재±∞처적겁한분별'태우"화"소우"기중간평형점시,초치문제적해수렴우일개련접량개은정평형점적파전해.최후,장결과응용도일개전염병모형.
This paper is concerned with the asymptotic behavior of classical solutions of a class of quasi-monotone reaction-diffusion systems. Under bistable assumption, the authors show that if only the spatial limits of the initial value at ±∞ are larger and smaller than the immediate unstable equilibrium respectively, then the solutions of the corresponding initial value problem will converge to a bistable traveling front. The approach is based on the elementary super- and sub-solution comparison and the convergence results of monotone semiflows. As an application, these abstract results are applied to a system modeling man-environment-man epidemics.