scholarly journals Vacuum isolating, blow up threshold, and asymptotic behavior of solutions for a nonlocal parabolic equation

2017 ◽  
Vol 58 (10) ◽  
pp. 101503 ◽  
Author(s):  
Xiaoliang Li ◽  
Baiyu Liu
Keyword(s):  
Asymptotic Behavior ◽  
Parabolic Equation ◽  
Blow Up ◽  
Asymptotic Behavior Of Solutions ◽  
Nonlocal Parabolic Equation

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 Large Solutions for Semilinear Parabolic Equations Involving Some Special Classes of Nonlinearities

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Constantin P. Niculescu ◽  
Ionel Rovenţa
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Blow Up ◽  
Neumann Boundary ◽  
Semilinear Parabolic Equations ◽  
New Class ◽  
Large Solutions ◽  
Nonlocal Parabolic Equation ◽  
Work Done ◽  
Semilinear Parabolic

We consider a new class of nonlinearities for which a nonlocal parabolic equation with Neumann boundary conditions has finite time blow-up solutions. Our approach is inspired by previous work done by Jazar and Kiwan (2008) and El Soufi et al. (2007).

scholarly journals Single blow-up solutions for a slightly subcritical biharmonic equation

2006 ◽  
Vol 2006 ◽  
pp. 1-20 ◽  
Author(s):  
Khalil El Mehdi
Keyword(s):  
Boundary Condition ◽  
Asymptotic Behavior ◽  
Critical Exponent ◽  
Critical Point ◽  
Bounded Domain ◽  
Biharmonic Equation ◽  
Blow Up ◽  
Asymptotic Behavior Of Solutions ◽  
Smooth Bounded Domain ◽  
Nondegenerate Critical Point

We consider a biharmonic equation under the Navier boundary condition and with a nearly critical exponent (Pε):∆2u=u9−ε,u>0inΩandu=∆u=0on∂Ω, whereΩis a smooth bounded domain inℝ5,ε>0. We study the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev quotient asεgoes to zero. We show that such solutions concentrate around a pointx0∈Ωasε→0, moreoverx0is a critical point of the Robin's function. Conversely, we show that for any nondegenerate critical pointx0of the Robin's function, there exist solutions of (Pε) concentrating aroundx0asε→0.

Blow-up for a nonlocal parabolic equation

2009 ◽  
Vol 71 (7-8) ◽  
pp. 3551-3562 ◽  
Author(s):  
Fei Liang ◽  
Yuxiang Li
Keyword(s):  
Parabolic Equation ◽  
Blow Up ◽  
Nonlocal Parabolic Equation
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