反應擴散方程的漸近周期解及行波解.pdf

1、華中科技大學博士學位論文反應擴散方程的漸近周期解及行波解姓名：王金良申請學位級別：博士專業(yè)：系統(tǒng)分析與集成指導教師：周笠20060405AbstractIn the study of the applied mathematics, it is very important to reveal the as-ymptotic behavior of the solutions for the differential equations

2、 and many researchershave been attracted to do so. For example, it is essential to know the evolution ofa population model as time goes on, since it is related to the serious problem of thespecies — to survive or to exti

3、nct. Usually, in order to reveal the asymptotic behaviorof the solution for a reaction-diffusion equation, it needs to prove the existence of thesteady-state solution or the periodic solution for the boundary value probl

4、em, yet it isimpossible for a nonperiodic time-varying system. Enlightened by the “weighted peri-odic”phenomenon, we consider these problems by another approach, that is, to studya particular asymptotic behavior—“asympto

5、tic weighted periodicity”. In addition, wehave also considered the existence of the wavefront solution (usually called travellingwave solution) which has special asymptotic behavior for the reaction-diffusion equa-tion i

6、n a multidimensional cylinder.For a population of a species, its density is affected not only by the environmentbut also by the time delays. In fact, there are so many factors may bring on time delaysto the evolution of

7、a population, such as the hatch period of the Aves, the gestationperiod of the mammals and the retarded supply of the food. What’s the asymptoticbehavior of a system with time delays? What about the effects of the time d

8、elays ona certain ecosystem? To answer these questions, we give a detailed discussion respectto the food-limited model and the competition model.It is known that a function f(t) is periodic if it satisfies f(t + T) = f(t

9、) for somepositive constant T. This kind of functions accords with the ideal movements of thesubstance in nature. Yet it is not always the case, such as the familiar damp vibrations.We take the swing of a single pendulum

10、 as an example. Let f(t) be the function ofthe swing angle. It should satisfies w(t) = f(t + T)/f(t) ?≡ 1 due to the resistanceof the air. In fact, w(t) satisfies 0 < w(t) < 1 in this case. We are enlightened bythi