Asymptotic behaviour of hessian equation with boundary blow up

2017 ◽  
Vol 33 (3) ◽  
pp. 575-586
Author(s):  
Lei-na Zhao ◽  
Zi-jian Liu
Keyword(s):  
Asymptotic Behaviour ◽  
Blow Up ◽  
Hessian Equation

Optimal global asymptotic behaviour of the solution to a class of singular Dirichlet problems

2020 ◽  
pp. 1-19
Author(s):  
Zhijun Zhang
Keyword(s):  
Asymptotic Behaviour ◽  
Unique Solution ◽  
Blow Up ◽  
Critical Values ◽  
Smooth Domain ◽  
Dirichlet Problems ◽  
Bounded Smooth Domain ◽  
Bounded Smooth

This paper is mainly concerned with the global asymptotic behaviour of the unique solution to a class of singular Dirichlet problems − Δu = b(x)g(u), u > 0, x ∈ Ω, u|∂Ω = 0, where Ω is a bounded smooth domain in ℝ n , g ∈ C1(0, ∞) is positive and decreasing in (0, ∞) with $\lim _{s\rightarrow 0^+}g(s)=\infty$ , b ∈ Cα(Ω) for some α ∈ (0, 1), which is positive in Ω, but may vanish or blow up on the boundary properly. Moreover, we reveal the asymptotic behaviour of such a solution when the parameters on b tend to the corresponding critical values.

Boundary blow-up solutions to the k-Hessian equation with singular weights

2021 ◽  
Vol 116 ◽  
pp. 106964
Author(s):  
Xinqiu Zhang ◽  
Lishan Liu
Keyword(s):  
Blow Up ◽  
Hessian Equation ◽  
Singular Weights

scholarly journals A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator

2020 ◽  
Vol 25 (1) ◽  
Author(s):  
Xinguang Zhang ◽  
Lishan Liu ◽  
Yonghong Wu ◽  
Yujun Cui
Keyword(s):  
Nonlinear Operator ◽  
Blow Up ◽  
Growth Conditions ◽  
Necessary Condition ◽  
Radial Solutions ◽  
Hessian Equation ◽  
Nonexistence And Existence ◽  
Sufficient And Necessary Condition

In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained. 

Boundary blow-up solutions to thek-Hessian equation with singular weights

2018 ◽  
Vol 167 ◽  
pp. 51-66 ◽  
Author(s):  
Xuemei Zhang ◽  
Meiqiang Feng
Keyword(s):  
Blow Up ◽  
Hessian Equation ◽  
Singular Weights

Equations de Schrödinger non linéaires en dimension deux

1979 ◽  
Vol 84 (3-4) ◽  
pp. 327-346 ◽  
Author(s):  
Thierry Cazenave
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Asymptotic Behaviour ◽  
Blow Up ◽  
Global Solutions ◽  
Two Dimensions ◽  
Linear Optics ◽  
Non Linear Optics ◽  
Non Linear ◽  
The Cauchy Problem

SynopsisThis paper is devoted to the study of some non linear Schrödinger equations in two dimensions, arising in non linear optics; in particular, it is concerned with solutions to the Cauchy problem. The problem of global existence and regularity of the solutions, the asymptotic behaviour of global solutions, and the blow-up of non global solutions are studied.

Asymptotic behaviour, uniqueness and stability of coexistence states of a non-cooperative reaction–diffusion model of nuclear reactors

2010 ◽  
Vol 140 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Rui Peng ◽  
Dong Wei ◽  
Guoying Yang
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Blow Up ◽  
Nuclear Reactors ◽  
Reaction Diffusion ◽  
Fast Neutrons ◽  
Fuel Temperature ◽  
Reaction Diffusion Model ◽  
Coexistence States ◽  
Spatial Dimensions

We investigate a non-cooperative reaction-diffusion model arising in the theory of nuclear reactors and are concerned with the associated steady-state problem. We determine the asymptotic behaviour of the coexistence states near the point of bifurcation from infinity, which exhibits the following very interesting spatial blow-up pattern: when the fuel temperature reaches a certain value, the free fast neutrons undergoing nuclear reaction will blow up in each spatial point of the interior of the reactor. Without any restriction on spatial dimensions, we also discuss the uniqueness and stability of the coexistence states. Our results complement and sharpen those derived in two recent works by Arioli and Lóopez-Gómez.

Blow up for a diffusion-advection equation

1989 ◽  
Vol 113 (3-4) ◽  
pp. 181-190 ◽  
Author(s):  
Nicholas D. Alikakos ◽  
Peter W. Bates ◽  
Christopher P. Grant
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Asymptotic Behaviour ◽  
Finite Time ◽  
Blow Up ◽  
Small Mass ◽  
Unit Interval ◽  
Advection Equation ◽  
Natural Question ◽  
Flux Boundary Conditions

SynopsisThese results describe the asymptotic behaviour of solutions to a certain non-linear diffusionadvection equation on the unit interval. The “no flux” boundary conditions prescribed result in mass being conserved by solutions and the existence of a mass-parametrised family of equilibria. A natural question is whether or not solutions stabilise to equilibria and if not, whether they blow up in finite time. Here it is shown that for non-linearities which characterise “fast association” there is a criticalmass such that initial data which have supercritical mass must lead to blow up in finite time. It is also shown that there exist initial data with arbitrarily small mass which also lead to blow up in finite time.

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