On partial differential equations of mixed type in N independent variables
It is proved that a large class of 2-nd order linear partial differential equations of mixed type in n independent variables can be solved by using the theory of positive symmetric systems of 1-st order partial differential equations. Some quasilinear equations of mixed type can be treated in the same way.
We study the photoinduced charge separation processes in solution through a pump–probe spectroscopy theory [Dah-Yen Yang and Sheh-Yi Sheu, J. Chem. Phys. 106, 9427 (1997)] numerically. We investigate the detailed mechanism of nonadiabatic transition processes via the transition differential flux analysis. For the harmonic potential surfaces, an electronic coherence motion is observed in the overdamped exothermic activationless and inverted regimes.