Quantum Euler-Poisson systems: global existence and exponential decay

Quantum Euler-Poisson Systems: Global Existence and Exponential Decay

A one-dimensional transient quantum Euler-Poisson system for the electron density, the current density and the electrostatic potential in bounded intervals is considered. The equations include the Bohm potential accounting for quantum mechanical effects and are of dispersive type. They are used, for instance, for the modeling of quantum semiconductor devices. The existence of local-in-time solu...

Quantum Euler-Poisson Systems: Existence of Stationary States

A one-dimensional quantum Euler-Poisson system for semiconductors for the electron density and the electrostatic potential in bounded intervals is considered. The existence and uniqueness of strong solutions with positive electron density is shown for quite general (possibly non-convex or non-monotone) pressure-density functions under a “subsonic” condition, i.e. assuming sufficiently small cur...

Mildly dissipative nonlinear Timoshenko systems — global existence and exponential stability

Exponential Decay in Quantum Mechanics

First of all: disregard all of so called “preliminary physical expectations”, because all these expectations are just a pseudonym for prejudices elaborated by the older generation. These words belong to Dirac, not to me. The right way of creating new physics is different: one should begin with a beautiful mathematical idea. But it should be really beautiful! No special relations to physics is c...

The existence and global exponential stability

Abstract By employing Schauder’s fixed point theorem and a non-Liapunov method (matrix theory, inequality analysis), we obtain some new criteria that ensure existence and global exponential stability of a periodic solution to a class of functional differential equations. Applying these criteria to a cellular neural network with time delays (delayed cellular neural network, DCNN) under a periodi...