Displaying similar documents to “On mixed problems for quasilinear second-order systems.”

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.

Convergence of a method for solving the magnetostatic field in nonlinear media

Jozef Kačur, Jindřich Nečas, Josef Polák, Jiří Souček (1968)

Aplikace matematiky

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For solving the boundary-value problem for potential of a stationary magnetic field in two dimensions in ferromagnetics it is possible to use a linearization based on the succesive approximations. In this paper the convergence of this method is proved under some conditions.

Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem

Karima Amoura, Christine Bernardi, Nejmeddine Chorfi (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns...