- 學位論文
反應擴散方程式行波解的變分結構
A Variational Formula for Traveling Wave Solutions of Reaction-diffusion Equations
並列摘要
In this essay, we find a variational structure of the bistable equation. We will show the existence of traveling wave solution by finding a critical point. The uniqueness of the speed of the bistable system is also obtained in this essay.
參考文獻
1. Joel Smoller.
Shock waves and reaction-diffusion equations, second edition, 1994, Springer-Verlag.
2. Aizik I. Volpert, Vitaly A. Volpert, Vladimir A. Volpert.
Traveling wave solutions of parabolic systems, 1991. Translation of Mathematical Monographs Vol 140, AMS.
Linear vs. Nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium. CPAM, vol 57, 2004.
延伸閱讀
- Chang, Y. T. (2010). 反應擴散方程的非平面傳動波 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2010.02667
- Kuo, C. H. (2005). 反應擴散方程及具微分項反應擴散方程之公式解及其應用 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2005.00700
- Chien, H. Y. (2012). 具非局部項之反應擴散方程的週期行波解 [master's thesis, National Taiwan University]. Airiti Library. https://doi.org/10.6342/NTU.2012.03124
- Yang, C. R. (2010). 反應擴散方程之進行波解的存在性 [doctoral dissertation, National Chiao Tung University]. Airiti Library. https://doi.org/10.6842/NCTU.2010.00507
- Yang, A. M., Yang, X. J., & Li, Z. B. (2013). Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets. Abstract and Applied Analysis, 2013(), 776-780-379. https://doi.org/10.1155/2013/351057