Hamilton-Jacobi方程解的定性分析

Qualitative Analysis of Hamilton-Jacobi Equation

考虑高维Hamilton-Jacobi方程的柯西问题,应用粘性解和特征线建立微分同胚映射,进而得到全局(局部)解存在性.

This paper considers the viscous solution for the Cauchy problems of high-dimensional Hamilton-Jacobi equation and builds the relations between the characteristic line and diffeomorphism to obtain the existence of the global（local）smooth solution.