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
for the critical case when
. Our results improve the ones
in [9,12].
Le Trong Thanh Bui, Anh Nguyen Dao, Jes\'us Ildefonso D\'iaz
Abstract:
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
for the critical case when
. 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 |
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Anh Nguyen Dao Applied Analysis Research Group Faculty of Mathematics and Statistics Ton Duc Thang University, Vietnam email: daonguyenanh@tdt.edu.vn |
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Jesús Ildefonso Díaz Instituto de Matematica Interdisciplinar Universidad Complutense de Madrid 28040 Madrid, Spain email: ildefonso.diaz@mat.ucm.es |
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