臺灣博碩士論文加值系統

常係數反應擴散方程的波型解長久以來已被廣泛地研究。Kolmogorov-Fisher型態的方程式有兩種基本型式，其中一種是非線性項有唯一零解的，另一種是非線性項有較高階零解的。這篇論文是在討論方程式u_t=u_{xx}+f(u), x is in (-infty, infty)
的解，當f(u)={e^{-1/u}}*(1-u), f(1)=0, f''(1)< 0
所採用的方法是利用單調性取u,t作為自變數，p(u,t)=u_x(x,t)作為應變數，並對p方程運用下解及上解之概念。

Wavefront solutions of scalar reaction-diffusion equations have been intensively studied for many years. There are two basic cases for the Kolmogorov-Fisher type equations, typified by a nonlinear term with simple zero root and a nonlinear term with higher order zero root. The paper is concerned with solutions u(x,t) of the equation
u_t=u_{xx}+f(u), x is in (-infty, infty)
in the case
f(u)={e^{-1/u}}*(1-u), f(1)=0, f''(1)< 0
The approach is to use the monotonicity to take u and t as
independent variables and p(u,t)=u_x(x,t) as the dependent
variable, and to apply ideas of sub- and super-solutions to the diffusion equation for p.

1. Introduction... 1~5
1.1. Background
1.2. The numerical results from four different kinds of
initial conditions
1.3. P-equation
1.4. Sub- and super-solutions
1.5. Comparison theorem for the p-equation

2. Exponentially decaying initial conditions...5~6
2.1. Sub-solution
2.2. Super-solution
2.3. Conclusion

3. Algebraically decaying initial conditions,alpha=1...6~14
3.1. Sub-solution for a> c_{crit}
3.2. Super-solution for a> c_{crit}
3.3. Conclusion

4. Algebraically decaying initial conditions,alpha>1...14~15
4.1. Sub-solution
4.2. Super-solution
4.3. Conclusion

5. Algebraically decaying initial conditions,alpha<1...15~17
5.1. Sub-solution
5.2. Super-solution
5.3. Initial conditions Phi not covered by the super-
solution overline{Psi}
5.4. Conclusion

6. Problem...18~21
6.1. Sub-solution
6.2. Super-solution
6.3. Conclusion

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