Quantization of the Blow-Up Value for the Liouville Equation with Exponential Neumann Boundary Condition

2018 ◽  
Vol 6 (1) ◽  
pp. 29-48 ◽  
Author(s):  
Tao Zhang ◽  
Changliang Zhou ◽  
Chunqin Zhou
Keyword(s):  
Boundary Condition ◽  
Liouville Equation ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Neumann Boundary

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.

HARDY-SOBOLEV INEQUALITY IN H1(Ω) AND ITS APPLICATIONS

2002 ◽  
Vol 04 (03) ◽  
pp. 409-434 ◽  
Author(s):  
ADIMURTHI
Keyword(s):  
Boundary Condition ◽  
Sobolev Inequality ◽  
Neumann Boundary Condition ◽  
Remainder Term ◽  
Blow Up ◽  
Neumann Boundary ◽  
Smooth Domain ◽  
Bounded Smooth Domain ◽  
Eigen Value ◽  
Bounded Smooth

In this article, we have determined the remainder term for Hardy–Sobolev inequality in H1(Ω) for Ω a bounded smooth domain and studied the existence, non existence and blow up of first eigen value and eigen function for the corresponding Hardy–Sobolev operator with Neumann boundary condition.

BLOW-UP ANALYSIS FOR SOLUTIONS OF THE LAPLACIAN EQUATION WITH EXPONENTIAL NEUMANN BOUNDARY CONDITION IN DIMENSION TWO

2006 ◽  
Vol 08 (06) ◽  
pp. 737-761 ◽  
Author(s):  
YU-XIA GUO ◽  
JIA-QUAN LIU
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Existence Theorem ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Neumann Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Laplacian Equation ◽  
Blow Up Analysis

We consider the asymptotic behavior of solutions of the Laplacian equation with exponential Neumann boundary condition in dimension two. As an application, we prove an existence theorem of nonminimum solutions.

scholarly journals Blow-up for the wave equation with nonlinear source and boundary damping terms

2015 ◽  
Vol 145 (4) ◽  
pp. 759-778 ◽  
Author(s):  
Alessio Fiscella ◽  
Enzo Vitillaro
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Initial Data ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
Neumann Boundary ◽  
Nonlinear Dissipation ◽  
Typical Problem ◽  
Nonlinear Source ◽  
Boundary Damping

The paper deals with blow-up for the solutions of an evolution problem consisting in a semilinear wave equation posed in a boundedC1,1open subset of ℝn, supplied with a Neumann boundary condition involving a nonlinear dissipation. The typical problem studied iswhere∂Ω=Γ0∪Γ1,Γ0∩Γ1= ∅,σ(Γ0) > 0, 2 <p≤ 2(n− 1)/(n− 2) (whenn≥ 3),m> 1,α∈L∞(Γ1),α≥ 0 andβ≥ 0. The initial data are posed in the energy space.The aim of the paper is to improve previous blow-up results concerning the problem.

scholarly journals Global $ C^2 $-estimates for smooth solutions to uniformly parabolic equations with Neumann boundary condition

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Zhenghuan Gao ◽  
Peihe Wang
Keyword(s):  
Boundary Condition ◽  
Parabolic Equations ◽  
Neumann Boundary Condition ◽  
Blow Up ◽  
A Priori Estimates ◽  
A Priori ◽  
Neumann Boundary ◽  
Smooth Solutions ◽  
Smooth Bounded Domain ◽  
Priori Estimates

<p style='text-indent:20px;'>In this paper, we establish global <inline-formula><tex-math id="M1">\begin{document}$ C^2 $\end{document}</tex-math></inline-formula> a priori estimates for solutions to the uniformly parabolic equations with Neumann boundary condition on the smooth bounded domain in <inline-formula><tex-math id="M2">\begin{document}$ \mathbb R^n $\end{document}</tex-math></inline-formula> by a blow-up argument. As a corollary, we obtain that the solutions converge to ones which move by translation. This generalizes the viscosity results derived before by Da Lio.</p>

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