Electron. J. Differential Equations, Vol. 2017 (2017), No. 176, pp. 1-8.

Critical case for the viscous Cahn-Hilliard equation

Le Trong Thanh Bui, Anh Nguyen Dao, Jes\'us Ildefonso D\'iaz

We prove the existence of solutions of the viscous Cahn-Hilliard equation in whole domain when the nonlinear term in the second order diffusion grows as $u^q$ for the critical case when $N\geq 3$. Our results improve the ones in [9,12].

Submitted April 30, 2016. Published July 11, 2017.
Math Subject Classifications: 35B25, 35K55, 35R25, 28A33, 35D99.
Key Words: Forward-backward parabolic equations; singular limits; pseudo-parabolic regularization; Cahn-Hilliard regularization; viscous Cahn-Hilliard equation.

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Le Trong Thanh Bui
Faculty of Mathematics and Computer Science
University of Science
Vietnam National University, Ho Chi Minh city
227 Nguyen Van Cu, D. 5, Ho Chi Minh city, Vietnam
email: bltthanh@hcmus.edu.vn
Anh Nguyen Dao
Applied Analysis Research Group
Faculty of Mathematics and Statistics
Ton Duc Thang University, Vietnam
email: daonguyenanh@tdt.edu.vn
Jesús Ildefonso Díaz
Instituto de Matematica Interdisciplinar
Universidad Complutense de Madrid
28040 Madrid, Spain
email: ildefonso.diaz@mat.ucm.es

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