On fractional heat equation

Abstract In this paper, the long-time behavior of the Cesaro mean of the fundamental solution for fractional Heat equation corresponding to random time changes in the Brownian motion is studied. We consider both stable subordinators leading to equations with the Caputo-Djrbashian fractional derivative and more general cases corresponding to differential-convolution operators, in particular, distributed order derivatives.

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Fundamental solution and long time behavior of the Porous Medium Equation in hyperbolic space

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2015.03.005 ◽

2015 ◽

Vol 104 (3) ◽

pp. 454-484 ◽

Cited By ~ 19

Author(s):

Juan Luis Vázquez

Keyword(s):

Porous Medium ◽

Fundamental Solution ◽

Hyperbolic Space ◽

Porous Medium Equation ◽

Time Behavior ◽

Long Time Behavior ◽

Medium Equation ◽

Long Time

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On the long time behavior of the stochastic heat equation

Probability Theory and Related Fields ◽

10.1007/s004400050226 ◽

1999 ◽

Vol 114 (3) ◽

pp. 279-289 ◽

Cited By ~ 12

Author(s):

Lorenzo Bertini ◽

Giambattista Giacomin

Keyword(s):

Heat Equation ◽

Stochastic Heat Equation ◽

Time Behavior ◽

Long Time Behavior ◽

Long Time ◽

The Stochastic Heat Equation

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The long time behavior of Brownian motion in tilted periodic potentials

Physica D Nonlinear Phenomena ◽

10.1016/j.physd.2014.12.008 ◽

2015 ◽

Vol 297 ◽

pp. 1-32 ◽

Cited By ~ 5

Author(s):

Liang Cheng ◽

Nung Kwan Yip

Keyword(s):

Brownian Motion ◽

Time Behavior ◽

Long Time Behavior ◽

Periodic Potentials ◽

Long Time

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Long Time Behavior of a Two-Phase Optimal Design for the Heat Equation

SIAM Journal on Control and Optimization ◽

10.1137/090780481 ◽

2010 ◽

Vol 48 (8) ◽

pp. 5333-5356 ◽

Cited By ~ 17

Author(s):

Grégoire Allaire ◽

Arnaud Münch ◽

Francisco Periago

Keyword(s):

Optimal Design ◽

Heat Equation ◽

Time Behavior ◽

Long Time Behavior ◽

Two Phase ◽

Long Time

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Long-Time Behavior of a Reaction–Diffusion Model with Strong Allee Effect and Free Boundary: Effect of Protection Zone

Journal of Dynamics and Differential Equations ◽

10.1007/s10884-021-10027-z ◽

2021 ◽

Author(s):

Ningkui Sun ◽

Chengxia Lei

Keyword(s):

Free Boundary ◽

Allee Effect ◽

Boundary Effect ◽

Reaction Diffusion ◽

Time Behavior ◽

Long Time Behavior ◽

Protection Zone ◽

Reaction Diffusion Model ◽

Long Time ◽

Strong Allee Effect

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On global dynamics of 2D convective Cahn–Hilliard equation

Boundary Value Problems ◽

10.1186/s13661-020-01477-3 ◽

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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The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

Asymptotic Analysis ◽

10.3233/asy-211703 ◽

2021 ◽

pp. 1-27

Author(s):

Ahmad Makki ◽

Alain Miranville ◽

Madalina Petcu

Keyword(s):

Fractal Dimension ◽

Boundary Conditions ◽

Well Posedness ◽

Time Behavior ◽

Long Time Behavior ◽

Dynamic Boundary Conditions ◽

Finite Dimensional ◽

Dynamic Boundary ◽

Long Time ◽

Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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