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Time-dependent electromagnetic waves in a cavity

Bo Kjellmert, Thomas Strömberg (2009)

Applications of Mathematics

The electromagnetic initial-boundary value problem for a cavity enclosed by perfectly conducting walls is considered. The cavity medium is defined by its permittivity and permeability which vary continuously in space. The electromagnetic field comes from a source in the cavity. The field is described by a magnetic vector potential 𝐀 satisfying a wave equation with initial-boundary conditions. This description through 𝐀 is rigorously shown to give a unique solution of the problem and is the starting...

Time-frequency analysis of Sjöstrand's class.

Karlheinz Gröchenig (2006)

Revista Matemática Iberoamericana

We investigate the properties an exotic symbol class of pseudodifferential operators, Sjöstrand's class, with methods of time-frequency analysis (phase space analysis). Compared to the classical treatment, the time-frequency approach leads to striklingly simple proofs of Sjöstrand's fundamental results and to far-reaching generalizations.

Time-optimal boundary control of an infinite order parabolic system with time lags

Adam Kowalewski, Anna Krakowiak (2008)

International Journal of Applied Mathematics and Computer Science

In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.

Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods

Eduard Feireisl (1988)

Aplikace matematiky

The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.

Topological asymptotic analysis of the Kirchhoff plate bending problem

Samuel Amstutz, Antonio A. Novotny (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed...

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