Displaying similar documents to “Semidiscretization for a nonlocal parabolic problem.”

Finite element approximation of a two-layered liquid film in the presence of insoluble surfactants

John W. Barrett, Linda El Alaoui (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a system of degenerate parabolic equations modelling a thin film, consisting of two layers of immiscible Newtonian liquids, on a solid horizontal substrate. In addition, the model includes the presence of insoluble surfactants on both the free liquid-liquid and liquid-air interfaces, and the presence of both attractive and repulsive van der Waals forces in terms of the heights of the two layers. We show that this system formally satisfies a Lyapunov structure, and a...

Classical global solutions of the initial boundary value problems for a class of nonlinear parabolic equations

Guo Wang Chen (1994)

Commentationes Mathematicae Universitatis Carolinae

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The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation u t = - A ( t ) u x 4 + B ( t ) u x 2 + g ( u ) x 2 + f ( u ) x + h ( u x ) x + G ( u ) with the initial boundary value conditions u ( - ℓ , t ) = u ( ℓ , t ) = 0 , u x 2 ( - ℓ , t ) = u x 2 ( ℓ , t ) = 0 , u ( x , 0 ) = ϕ ( x ) , or with the initial boundary value conditions u x ( - ℓ , t ) = u x ( ℓ , t ) = 0 , u x 3 ( - ℓ , t ) = u x 3 ( ℓ , t ) = 0 , u ( x , 0 ) = ϕ ( x ) , are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.