Well posedness and smoothing effect of Schrödinger-Poisson equation
Well posedness and smoothing effect of Schrödinger-Poisson equation
In this work we take under consideration the Cauchy problem for the Schrödinger-Poisson type equation i∂tu=−∂x2u+V(u)u−f(∣u∣2)u, where f represents a local nonlinear interaction (we take into account both attractive and repulsive models) and V is taken as a suitable solution of the Poisson equation V=1∕2∣x∣∗(C−∣u∣2), C∊Cc∞ is the doping profile …