Page 1

Displaying 1 – 17 of 17

Showing per page

Relaxation-time limits of global solutions in full quantum hydrodynamic model for semiconductors

Sungjin Ra, Hakho Hong (2024)

Applications of Mathematics

This paper is concerned with the global well-posedness and relaxation-time limits for the solutions in the full quantum hydrodynamic model, which can be used to analyze the thermal and quantum influences on the transport of carriers in semiconductor devices. For the Cauchy problem in 3 , we prove the global existence, uniqueness and exponential decay estimate of smooth solutions, when the initial data are small perturbations of an equilibrium state. Moreover, we show that the solutions converge into...

Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica (2003)

Journées équations aux dérivées partielles

We concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound from below the blow-up rate for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

Valeria Banica (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than ( T - t ) - 1 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients

Kenichi Ito, Shu Nakamura (2012)

Annales de l’institut Fourier

We consider Schrödinger operators H on n with variable coefficients. Let H 0 = - 1 2 be the free Schrödinger operator and we suppose H is a “short-range” perturbation of H 0 . Then, under the nontrapping condition, we show that the time evolution operator: e - i t H can be written as a product of the free evolution operator e - i t H 0 and a Fourier integral operator W ( t ) which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators. These results...

Currently displaying 1 – 17 of 17

Page 1