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Regularity of solutions for a sixth order nonlinear parabolic equation in two space dimensions

100%
Liu C.
Annales Polonici Mathematici
|
2013
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tom 107
|
nr 3
271-291
EN
We consider an initial-boundary problem for a sixth order nonlinear parabolic equation, which arises in oil-water-surfactant mixtures. Using Schauder type estimates and Campanato spaces, we prove the global existence of classical solutions for the problem in two space dimensions.
2
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On the Convective Cahn-Hilliard Equation

100%
Liu C.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2005
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tom 53
|
nr 3
299-314
EN
The author studies the convective Cahn-Hilliard equation. Some results on the existence of classical solutions and asymptotic behavior of solutions are established. The instability of the traveling waves is also discussed.
3
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Global Attractor for the Convective Cahn-Hilliard Equation

63%
Zhao X., Liu C.
Bulletin of the Polish Academy of Sciences. Mathematics
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2010
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tom 58
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nr 2
117-127
EN
This paper is concerned with the convective Cahn-Hilliard equation. We use a classical theorem on existence of a global attractor to derive that the convective Cahn-Hilliard equation possesses a global attractor on some subset of H².
4
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Weak Solutions for a Fourth Order Degenerate Parabolic Equation

63%
Liu C., Guo J.
Bulletin of the Polish Academy of Sciences. Mathematics
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2006
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tom 54
|
nr 1
27-39
EN
We consider an initial-boundary value problem for a fourth order degenerate parabolic equation. Under some assumptions on the initial value, we establish the existence of weak solutions by the discrete-time method. The asymptotic behavior and the finite speed of propagation of perturbations of solutions are also discussed.
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