scholarly journals Blow up for the solutions of the pressureless Euler-Poisson equations with time-dependent damping

2021 ◽  
Author(s):  
Jianli Liu ◽  
Jingwei Wang ◽  
Lining Tong
Keyword(s):  
Plasma Physics ◽  
Formation Mechanism ◽  
Blow Up ◽  
Time Dependent ◽  
Singularity Formation ◽  
Poisson Equations ◽  
Repulsive Forces ◽  
Physical Phenomena ◽  
Semiconductor Modeling

The Euler-Poisson equations can be used to describe the important physical phenomena in many areas, such as semiconductor modeling and plasma physics. In this paper, we show the singularity formation mechanism for the solutions of the pressureless Euler-Poisson equations with time-dependent damping for the attractive forces in R^n (n ≧1) and the repulsive forces in R. We obtain the blow up of the derivative of the velocity under the appropriate assumptions.

scholarly journals Stabilities for Nonisentropic Euler-Poisson Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Ka Luen Cheung ◽  
Sen Wong
Keyword(s):  
Energy Method ◽  
Finite Time ◽  
Blow Up ◽  
Classical Solutions ◽  
Poisson Equations ◽  
Repulsive Forces

We establish the stabilities and blowup results for the nonisentropic Euler-Poisson equations by the energy method. By analysing the second inertia, we show that the classical solutions of the system with attractive forces blow up in finite time in some special dimensions when the energy is negative. Moreover, we obtain the stabilities results for the system in the cases of attractive and repulsive forces.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Blow-up for the compressible isentropic Navier-Stokes-Poisson equations

2019 ◽  
Vol 70 (1) ◽  
pp. 9-19
Author(s):  
Jianwei Dong ◽  
Junhui Zhu ◽  
Yanping Wang
Keyword(s):  
Blow Up ◽  
Navier Stokes ◽  
Poisson Equations

Application of Terahertz Spectroscopy to Time-Dependent Chemical-Physical Phenomena

2009 ◽  
Vol 113 (34) ◽  
pp. 9418-9423 ◽  
Author(s):  
Plinio Innocenzi ◽  
Luca Malfatti ◽  
Massimo Piccinini ◽  
Diego Sali ◽  
Ulrich Schade ◽  
...  
Keyword(s):  
Terahertz Spectroscopy ◽  
Time Dependent ◽  
Physical Phenomena

scholarly journals Reconstructing the Scene: New Views of Supernovae and Progenitors from the SNSPOL Project

2016 ◽  
Vol 12 (S329) ◽  
pp. 54-58
Author(s):  
Jennifer L. Hoffman ◽  
G. Grant Williams ◽  
Douglas C. Leonard ◽  
Christopher Bilinski ◽  
Luc Dessart ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Electron Scattering ◽  
Time Dependent ◽  
Complex Velocity ◽  
Circumstellar Material ◽  
Radiative Transfer Models ◽  
The Future ◽  
Geometrical Information ◽  
Physical Phenomena ◽  
Over Time

AbstractBecause polarization encodes geometrical information about unresolved scattering regions, it provides a unique tool for analyzing the 3-D structures of supernovae (SNe) and their surroundings. SNe of all types exhibit time-dependent spectropolarimetric signatures produced primarily by electron scattering. These signatures reveal physical phenomena such as complex velocity structures, changing illumination patterns, and asymmetric morphologies within the ejecta and surrounding material. Interpreting changes in polarization over time yields unprecedentedly detailed information about supernovae, their progenitors, and their evolution.Begun in 2012, the SNSPOL Project continues to amass the largest database of time-dependent spectropolarimetric data on SNe. I present an overview of the project and its recent results. In the future, combining such data with interpretive radiative transfer models will further constrain explosion mechanisms and processes that shape SN ejecta, uncover new relationships among SN types, and probe the properties of progenitor winds and circumstellar material.

scholarly journals Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity

2019 ◽  
Vol 62 (2) ◽  
pp. 157-189 ◽  
Author(s):  
Kazumasa Fujiwara ◽  
Masahiro Ikeda ◽  
Yuta Wakasugi
Keyword(s):  
Wave Equation ◽  
Blow Up ◽  
Time Dependent ◽  
Power Type

scholarly journals The Singularity Formation on the Coupled Burgers–Constantin–Lax–Majda System with the Nonlocal Term

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Linrui Li ◽  
Shu Wang
Keyword(s):  
Initial Data ◽  
Finite Time ◽  
Smooth Solution ◽  
Blow Up ◽  
Nonlocal Term ◽  
Convection Term ◽  
Large Initial Data ◽  
Singularity Formation ◽  
Time Singularity ◽  
Finite Time Singularity

In this paper, we study the finite-time singularity formation on the coupled Burgers–Constantin–Lax–Majda system with the nonlocal term, which is one nonlinear nonlocal system of combining Burgers equations with Constantin–Lax–Majda equations. We discuss whether the finite-time blow-up singularity mechanism of the system depends upon the domination between the CLM type’s vortex-stretching term and the Burgers type’s convection term in some sense. We give two kinds of different finite-time blow-up results and prove the local smooth solution of the nonlocal system blows up in finite time for two classes of large initial data.

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