scholarly journals Global existence and nonlinear stability for the relativistic Vlasov-Poisson system in the gravitational case

2007 ◽  
Vol 56 (5) ◽  
pp. 2453-2488 ◽  
Author(s):  
Mahir Hadzic ◽  
Gerhard Rein
Keyword(s):  
Global Existence ◽  
Nonlinear Stability ◽  
Poisson System

Stability of disk-like galaxies – Part II: The Kuzmin disk

Analysis ◽  
2007 ◽  
Vol 27 (4) ◽  
Author(s):  
Roman Fiřt
Keyword(s):  
Steady State ◽  
Nonlinear Stability ◽  
Variational Approach ◽  
Poisson System ◽  
Finite Mass

SummaryWe prove the existence and nonlinear stability of the Kuzmin disk, a polytropic steady state of the Vlasov–Poisson system widely used in astrophysics, which has infinite support, but finite mass. As in Part I we use the variational approach by REIN and GUO.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR FOR A SEMICONDUCTOR DRIFT-DIFFUSION-POISSON MODEL

2008 ◽  
Vol 18 (03) ◽  
pp. 443-487 ◽  
Author(s):  
HAO WU ◽  
PETER A. MARKOWICH ◽  
SONGMU ZHENG
Keyword(s):  
Global Existence ◽  
Existence And Uniqueness ◽  
Poisson Model ◽  
Stationary Problem ◽  
Time Dependent ◽  
Unique Equilibrium ◽  
Poisson System ◽  
Drift Diffusion ◽  
Global Existence And Uniqueness ◽  
Time Dependent Problem

In this paper a time-dependent as well as a stationary drift-diffusion-Poisson system for semiconductors are studied. Global existence and uniqueness of weak solution of the time-dependent problem are proven and we also prove the existence and uniqueness of the steady state. It is shown that as time tends to infinity, the solution of the time-dependent problem will converge to a unique equilibrium. Due to the presence of recombination-generation rate R in our drift-diffusion-Poisson model, the work of this paper in some sense extends the results in the previous literature (on both time-dependent problem and stationary problem).

SOME ASYMPTOTICS FOR A REACTIVE NAVIER–STOKES–POISSON SYSTEM

1999 ◽  
Vol 09 (07) ◽  
pp. 1039-1076 ◽  
Author(s):  
B. DUCOMET
Keyword(s):  
Global Existence ◽  
Global Solution ◽  
Spherical Model ◽  
Navier Stokes ◽  
Positive Energy ◽  
Stability Of Solutions ◽  
Poisson System ◽  
Rigid Core ◽  
Existence And Stability

We prove global existence and stability of solutions for a spherical model of reactive compressible self-gravitating fluid when a rigid core is present. In the absence of core, we show that no global solution of positive energy can exist.

scholarly journals A system of Schrödinger equations with general quadratic-type nonlinearities

2020 ◽  
pp. 2050023
Author(s):  
Norman Noguera ◽  
Ademir Pastor
Keyword(s):  
Global Existence ◽  
Variational Methods ◽  
Nonlinear Stability ◽  
Ground State ◽  
Finite Time ◽  
Blow Up ◽  
Quadratic Growth ◽  
Schrodinger Equations ◽  
Concentration Compactness ◽  
Schrödinger Equations

In this work, we study a system of Schrödinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in terms of the ground state solutions associated with the corresponding elliptic system, which in turn are obtained by applying variational methods. By using the concentration-compactness method we also investigate the nonlinear stability/instability of the ground states.

Sign in / Sign up

Export Citation Format

Share Document