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.
Linear vs. Nonlinear selection for the propagation speed of the solutions of scalar reaction-diffusion equations invading an unstable equilibrium. CPAM, vol 57, 2004.
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
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
Li, C. M. (2011). 非靜態反應-對流-擴散方程的高階緊緻有限差分解法 [master's thesis, National Central University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0031-1903201314411610