Electron. J. Differential Equations, Vol. 2020 (2020), No. 07, pp. 1-15.

Passing to the limit on small parameters for generalized viscous Cahn-Hilliard type equations with nonlinear source

Bui Le Trong Thanh, Nguyen Ngoc Quoc Thuong

We study the well-posedness of the generalized viscous Cahn-Hilliard equation with nonlinear source term. Then, we analyze the singular limits when the relaxed terms vanish. In the sense of Young measures, we obtain the measure-valued solution of a forward-backward parabolic type equation.

Submitted July 7, 2019. Published January 13, 2020.
Math Subject Classifications: 35B25, 35K55, 35R25, 28A33, 35D99.
Key Words: Generalized Cahn-Hilliard equation; singular limits; forward-backward parabolic equations; Young measure.

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Bui Le Trong Thanh
Faculty of Mathematics and Computer Science
University of Science
227 Nguyen Van Cu, D. 5, Ho Chi Minh City, Vietnam
email: bltthanh@hcmus.edu.vn
Nguyen Ngoc Quoc Thuong
Faculty of Mathematics and Statistics
Quy Nhon University
170 An Duong Vuong Street, Quy Nhon City, Vietnam
email: nguyenngocquocthuong@qnu.edu.vn

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