This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines. Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that is unbounded from below and that it has a sequence of negative eigenvalues tending to . Using the Min-Max principle, a characterization of its positive eigenvalues is given. Thanks to this characterization, some conditions...
This paper is devoted to the spectral analysis of a non elliptic operator , deriving from the study of superconducting micro-strip lines.
Once a sufficient condition for the self-adjointness of operator has been derived, we determine its continuous spectrum. Then, we show that
is unbounded from below and that it has a sequence of negative eigenvalues tending to -∞. Using the Min-Max principle, a characterization of
its positive eigenvalues is given. Thanks to this characterization, some conditions...
We consider the approximation of a class of
exponentially stable infinite dimensional linear systems modelling
the damped vibrations of one dimensional vibrating systems or of
square plates. It is by now well known that the approximating
systems obtained by usual finite element or finite difference are
not, in general, uniformly stable with respect to the discretization
parameter. Our main result shows that, by adding a suitable
numerical viscosity term in the numerical scheme, our approximations
are...
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