Volume 27, Issue 2
Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential

Commun. Math. Res., 27 (2011), pp. 156-168.

Published online: 2021-05

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• Abstract

In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the $L^p$ type estimates and the theory of Morrey spaces, we prove the Hölder continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.

35K55, 35G20, 35G30

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@Article{CMR-27-156, author = {Huang , RuiYin , Jingxue and Wang , Liangwei}, title = {Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {2}, pages = {156--168}, abstract = {

In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the $L^p$ type estimates and the theory of Morrey spaces, we prove the Hölder continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19100.html} }
TY - JOUR T1 - Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential AU - Huang , Rui AU - Yin , Jingxue AU - Wang , Liangwei JO - Communications in Mathematical Research VL - 2 SP - 156 EP - 168 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19100.html KW - Cahn-Hilliard equation, concentration dependent mobility, gradient dependent potential. AB -

In this paper we consider the initial boundary value problem of Cahn-Hilliard equation with concentration dependent mobility and gradient dependent potential. By the $L^p$ type estimates and the theory of Morrey spaces, we prove the Hölder continuity of the solutions. Then we obtain the existence of global classical solutions. The present work can be viewed as an extension to the previous work on the Cahn-Hilliard equation with concentration dependent mobility and potential.

Rui Huang, Jingxue Yin & Liangwei Wang. (2021). Two Dimensional Cahn-Hilliard Equation with Concentration Dependent Mobility and Gradient Dependent Potential. Communications in Mathematical Research . 27 (2). 156-168. doi:
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