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A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form , one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.
Transport phenomena of minority carriers in quasi neutral regions of heavily doped semiconductors are considered for the case of one-dimensional stationary flow and their study is reduced to a Fredholm integral equation of the second kind, the kernel and the known term of which are built from known functions of the doping arbitrarily distributed in space. The advantage of the method consists, among other things, in having all the coefficients of the differential equations and of the boundary conditions...
We consider the exact controllability and stabilization of Maxwell
equation by using results on the propagation of singularities of the
electromagnetic field. We will assume geometrical control condition and use
techniques of the work of Bardos et al. on the wave
equation. The problem of internal stabilization will be treated with more
attention because the condition divE=0 is not preserved by the system of
Maxwell with Ohm's law.
A Discontinuous Galerkin method is used for to the numerical solution of the time-domain Maxwell equations on unstructured meshes. The method relies on the choice of local basis functions, a centered mean approximation for the surface integrals and a second-order leap-frog scheme for advancing in time. The method is proved to be stable for cases with either metallic or absorbing boundary conditions, for a large class of basis functions. A discrete analog of the electromagnetic energy is conserved...
A Discontinuous Galerkin method is used for to the
numerical solution of the time-domain Maxwell equations on
unstructured meshes. The method relies on the choice of local basis
functions, a centered mean approximation for the surface integrals
and a second-order leap-frog scheme for advancing in time. The method
is proved to be stable for cases with either metallic or absorbing
boundary conditions, for a large class of basis functions. A
discrete analog of the electromagnetic energy is conserved...
As an example of a simple constrained geometric non-linear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semi-discrete scheme based on finite elements and prove its convergence in space dimension 2 for initial data of finite energy.
As an example of a simple constrained geometric non-linear wave equation, we study a numerical approximation of the Maxwell Klein Gordon equation. We consider an existing constraint preserving semi-discrete scheme based on finite elements and prove its convergence in space dimension 2 for initial data of finite energy.
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.
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