Long-time behavior of nonlinear integro-differential evolution equations

2013 ◽  
Vol 91 ◽  
pp. 20-31 ◽  
Author(s):  
Justino Sánchez ◽  
Vicente Vergara
Keyword(s):  
Differential Evolution ◽  
Evolution Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

TIP INSTABILITY DURING CONFINED DIFFUSION-LIMITED GROWTH

1988 ◽  
Vol 02 (08) ◽  
pp. 945-951 ◽  
Author(s):  
DAVID A. KESSLER ◽  
HERBERT LEVINE
Keyword(s):  
Evolution Equations ◽  
Dynamical Behavior ◽  
Stable Steady State ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Limited Growth ◽  
Channel Geometry ◽  
Diffusion Limited ◽  
Long Time

We study diffusion-limited crystal growth in a two dimensional channel geometry. We demonstrate that although there exists a linearly stable steady-state finger solution of the pattern evolution equations, the true dynamical behavior can be controlled by a tip-widening instability. Possible scenarios for the long-time behavior of the system are presented.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

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