A new global Carleman estimate for Cahn-Hilliard type equation and its applications
type: Item
instance of: scholarly article
title: A new global Carleman estimate for Cahn-Hilliard type equation and its applications
zbMATH Open document ID: 1334.35080
author: Peng Gao
published in: Journal of Differential Equations
publication date: 2015-11-04T00:00:00Z
review text: In this article, the author considers a class of parabolic fourth-order problems of the type \[ \begin{alignedat}{2} \partial_t y + \partial_{xxxx} y & = f_0 + \partial_x f_1 + \partial_{xx} f_2 & \quad & \text{in } (0,1)\times (0,T),\\ y(0,t) & = 0 = y(1,t) & \quad & \text{in } (0,T),\\ \partial_x y(0,t) & = 0 = \partial_{x} y(1,t) & \quad & \text{in } (0,T),\\ y(x,0) & = y_0(x) & \quad & \text{in } (0,1). \end{alignedat} \] For this class of equations, he proves a Carleman inequality. In the case in which \[ f_0=a y, \;f_1 = by, \;f_2 = c y, \] with \(a,b,c\in L^{\infty}([0,1]\times[0,T])\), he deduces the weak unique continuation property for solutions to the problem at hand. Finally, the author derives an interior controllability result for a semilinear version of the equation.
reviewed by: Angkana Rüland
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 6504559
zbMATH Keywords: global Carleman estimate
zbMATH Keywords: Cahn-Hilliard type equation
zbMATH Keywords: unique continuation property
zbMATH Keywords: null controllability
MaRDI profile type: Publication
full work available at URL: j.jde.2015.08.053
OpenAlex ID: W2209977796
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DOI: 10.1016/J.JDE.2015.08.053
description: scientific article; zbMATH DE number 6504559