Generalized impedance boundary conditions for strongly absorbing obstacle: The full wave equation
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Multiscale or multiphysics partial differential equations are used to model a wide range of physical systems with various applications, e.g. from material and natural science to problems in biology or engineering. When the ratio between the smallest scale ...
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Cloaking via transformation optics was introduced by Pendry, Schurig, and Smith for the
Maxwell system and Leonhardt in the geometric optics setting. They used a singular change
of variables which blows up a point into a cloaked region. The same transforma ...
We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on R3+1 constructed in [28], [27] are stable along a co-dimension three manifold of radial data perturbations in a suit ...
Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...
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A family of effective equations for the wave equation in locally periodic media over long time is derived. In particular, explicit formulas for the effective tensors are provided. To validate the derivation, an a priori error estimate between the effective ...
Selective noise amplifiers are characterized by large linear amplification to external perturbations in a particular frequency range despite their global linear stability. Applying a stochastic forcing with increasing amplitude, the response undergoes a st ...
It is a well-known fact that small-amplitude perturbations can be amplified in globally stable flows due to non-normal mechanisms. This leads in the time domain to the transient growth of some initial disturbances, and in the frequency domain to the amplif ...
This paper concerns approximate cloaking by mapping for a full, but scalar wave equation, when one allows for physically relevant frequency dependence of the material properties of the cloak. The paper is a natural continuation of [20], but here we employ ...