An Initial Value Problem from Semiconductor Device Theory
M. S. Mock · SIAM Journal on Mathematical Analysis · 1974
A system of three quasi-linear partial differential equations is considered, as a simplified model of the transport of mobile carriers in a semiconductor device. Assuming a convenient form of the boundary conditions, it is shown that the initial value problem is well-posed, and that the steady state solution is unique and stable. A finite difference approximation preserving reasonable bounds on the numerical solutions is also described.