scholarly journals Blowup Phenomena for the Compressible Euler and Euler-Poisson Equations with Initial Functional Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Sen Wong ◽  
Manwai Yuen
Keyword(s):  
Boundary Condition ◽  
Life Span ◽  
Finite Time ◽  
Blow Up ◽  
Symmetric Case ◽  
Governing Equations ◽  
Pressure Function ◽  
Poisson Equations ◽  
Compressible Euler ◽  
Blowup Result

We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations inRN. For timet≥0, we can define a functionalH(t)associated with the solution of the equations and some testing functionf. When the pressure functionPof the governing equations is of the formP=Kργ, whereρis the density function,Kis a constant, andγ>1, we can show that the nontrivialC1solutions with nonslip boundary condition will blow up in finite time ifH(0)satisfies some initial functional conditions defined by the integrals off. Examples of the testing functions includerN-1ln(r+1),rN-1er,rN-1(r3-3r2+3r+ε),rN-1sin((π/2)(r/R)), andrN-1sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.

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.

NUMERICAL BLOW-UP FOR A NONLINEAR PROBLEM WITH A NONLINEAR BOUNDARY CONDITION

2002 ◽  
Vol 12 (04) ◽  
pp. 461-483 ◽  
Author(s):  
RAÚL FERREIRA ◽  
PABLO GROISMAN ◽  
JULIO D. ROSSI
Keyword(s):  
Boundary Condition ◽  
Heat Equation ◽  
Nonlinear Problem ◽  
Finite Time ◽  
Numerical Scheme ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Blow Up ◽  
Nonlinear Heat Equation ◽  
Mesh Parameter

In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero.

Blow-up for a parabolic system coupled in an equation and a boundary condition

2001 ◽  
Vol 131 (6) ◽  
pp. 1345-1355 ◽  
Author(s):  
Keng Deng ◽  
Cheng-Lin Zhao
Keyword(s):  
Boundary Condition ◽  
Parabolic System ◽  
Finite Time ◽  
Blow Up ◽  
All Solutions ◽  
Image Position

In this paper, we consider non-negative solutions of , We prove that if pq ≤ 1, every solution is global while if pq > 1, all solutions blow up in finite time. We also show that if p, q ≥ 1, then blow-up can occur only on the boundary.

scholarly journals Sharp thresholds of blow-up and global existence for the Schrödinger equation with combined power-type and Choquard-type nonlinearities

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yongbin Wang ◽  
Binhua Feng
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Critical Case ◽  
Blow Up ◽  
Critical Mass ◽  
Choquard Equation ◽  
Power Type ◽  
Scale Invariant ◽  
Nonlinear Schrödinger ◽  
Sharp Thresholds

AbstractIn this paper, we consider the sharp thresholds of blow-up and global existence for the nonlinear Schrödinger–Choquard equation $$ i\psi _{t}+\Delta \psi =\lambda _{1} \vert \psi \vert ^{p_{1}}\psi +\lambda _{2}\bigl(I _{\alpha } \ast \vert \psi \vert ^{p_{2}}\bigr) \vert \psi \vert ^{p_{2}-2}\psi . $$iψt+Δψ=λ1|ψ|p1ψ+λ2(Iα∗|ψ|p2)|ψ|p2−2ψ. We derive some finite time blow-up results. Due to the failure of this equation to be scale invariant, we obtain some sharp thresholds of blow-up and global existence by constructing some new estimates. In particular, we prove the global existence for this equation with critical mass in the $L^{2}$L2-critical case. Our obtained results extend and improve some recent results.

scholarly journals Blow-Up Analysis for a Quasilinear Parabolic Equation with Inner Absorption and Nonlinear Neumann Boundary Condition

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Zhong Bo Fang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Quasilinear Parabolic Equation ◽  
Neumann Boundary ◽  
Initial Boundary ◽  
Blow Up Analysis ◽  
Inner Absorption ◽  
Quasilinear Parabolic

We investigate an initial-boundary value problem for a quasilinear parabolic equation with inner absorption and nonlinear Neumann boundary condition. We establish, respectively, the conditions on nonlinearity to guarantee thatu(x,t)exists globally or blows up at some finite timet*. Moreover, an upper bound fort*is derived. Under somewhat more restrictive conditions, a lower bound fort*is also obtained.

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
Sign in / Sign up

Export Citation Format

Share Document