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MSC 2010: 45DB05, 45E05, 78A45We show that a certain axisymmetric hypersingular integral equation arising in problems of cracks in the elasticity theory may be explicitly solved in the case where the crack occupies a plane circle. We give three different forms of the resolving formula. Two of them involve regular kernels, while the third one involves a singular kernel, but requires less regularity assumptions on the the right-hand side of the equation.
A special two-sided condition for the incremental magnetic reluctivity is introduced which guarantees the unique existence of both the weak and the approximate solutions of the nonlinear stationary magnetic field distributed on a region composed of different media, as well as a certain estimate of the error between the two solutions. The condition, being discussed from the physical as well as the mathematical point of view, can be easily verified and is fulfilled for various magnetic reluctivity...
Mathematics Subject Classification 2010: 45DB05, 45E05, 78A45.We give a procedure to reduce a hypersingular integral equation, arising
in 2d diffraction problems on cracks in elastic media, to a Fredholm integral
equation of the second kind, to which it is easier and more effectively to
apply numerical methods than to the initial hypersingular equation.
Some new mathematical results of existence and uniqueness of solutions are obtained for a class of quasi-variational inequalities modeling the free boundary problem for the determination of the depletion zone in reverse biased semiconductor diodes. The corresponding one (or two) obstacle implicit problems are solved by direct methods with weak regularity estimates for mixed boundary value elliptic problems of second order.
We prove that penalization of constraints occuring in the linear elliptic Neumann problem yields directly the exact solution for an arbitrary set of penalty parameters. In this case there is a continuum of Lagrange's multipliers. The proposed penalty method is applied to calculate the magnetic field in the window of a transformer.
In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...
In this paper, we consider general nonlinear systems with observations,
containing a (single) unknown function φ. We study the possibility to
learn about this unknown function via the observations: if it is possible to
determine the [values of the] unknown function from any experiment [on the set
of states visited during the experiment], and for any arbitrary input
function, on any time interval, we say that the system is “identifiable”.
For systems without controls, we give a more or less complete...
We give a geometric descriptions of (wave) fronts in wave propagation processes. Concrete form of defining function of wave front issued from initial algebraic variety is obtained by the aid of Gauss-Manin systems associated with certain complete intersection singularities. In the case of propagations on the plane, we get restrictions on types of possible cusps that can appear on the wave front.
In this paper, we consider linear ordinary differential equations originating in
electronic engineering, which exhibit exceedingly rapid
oscillation. Moreover, the oscillation model is completely different
from the familiar framework of asymptotic analysis of highly
oscillatory integrals. Using a Bessel-function identity, we expand the oscillator into
asymptotic series, and this allows us to extend Filon-type approach
to this setting. The outcome is a time-stepping method that guarantees
...
Energy functionals for the Preisach hysteresis operator are used for proving the existence of weak periodic solutions of the one-dimensional systems of Maxwell equations with hysteresis for not too large right-hand sides. The upper bound for the speed of propagation of waves is independent of the hysteresis operator.
The author proves the existence of solution of Van Roosbroeck's system of partial differential equations from the theory of semiconductors. His results generalize those of Mock, Gajewski and Seidman.
In this work, we propose the Shannon wavelets approximation for the numerical solution of a class of integro-differential equations which describe the charged particle motion for certain configurations of oscillating magnetic fields. We show that using the Galerkin method and the connection coefficients of the Shannon wavelets, the problem is transformed to an infinite algebraic system, which can be solved by fixing a finite scale of approximation. The error analysis of the method is also investigated....
The paper deals with the computation of Aden functions. It gives estimates of errors for the computation of Aden functions by downward reccurence.
The paper deals with the computation of Riccati-Bessel functions. A modification of Miller method is presented together with estimates of relative errors.
We consider the Laplace operator in a thin tube of
with a Dirichlet condition on its boundary. We study asymptotically the spectrum of
such an operator as the thickness of the tube's cross section goes to zero. In particular we
analyse how the energy levels depend simultaneously on the curvature of the tube's central axis
and on the rotation of the cross section with respect to the Frenet frame. The main argument is a
Γ-convergence theorem for a suitable sequence of quadratic energies.
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