In 1982, the Belgian Pilots' Guild raised the question of what effect exposure to radar radiation--for example, that encountered in passing a pilot launch's radar--might have on the human body. Recapitulating investigations of this question, this article states that in 25 years of experience with radar, there have been no known incidents of pilots being affected by radar waves. In the future, however, involvement by some pilots with Vessel Traffic Service shore-based radar could affect pilots somewhat differently from limited exposure to pilot launch radar. Pilots who find themselves in new working conditions close to an emitting source should exercise care all times.

About heat waves

The heat equation also shows what a PDE is in general: We are given some kind of relationship between a function u(x,t) and/or its partial derivatives. In the one dimensional case this can be partial derivatives in time t or in space x. The problem is to find functions u(x,t) which satisfy the given relationship and sometimes satisfy additional conditions (initital value conditions or boundary conditions).

The One-Dimensional Heat Equation

The paper deals with the explicit calculus and the properties of the fundamental solution K of a parabolic operator related to a semilinear equation that models reaction diffusion systems with excitable kinetics. The initial value problem in all of the space is analyzed together with continuous dependence and a priori estimates of the solution. These estimates show that the asymptotic behavior is determined by the reaction mechanism. Moreover it’s possible a rigorous singular perturbation analysis for discussing travelling waves with their characteristic times.

Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation

Existence and uniqueness of solutions of a class of third order dissipative problems with various boundary conditions describing the Josephson effect

The paper deals with an integrodifferential operator which models numerous phenomena in superconductivity, in biology and in viscoelasticity. Initialboundary value problems with Neumann, Dirichlet and mixed boundary conditions are analyzed. An asymptotic analysis is achieved proving that for large t, the in uences of the initial data vanish, while the effects of boundary disturbances are everywhere bounded.

Asymptotic estimates related to an integro differential equation

The paper deals with a third order semilinear equation which characterizes exponentially shaped Josephson junctions in superconductivity. The initial-boundary problem with Dirichlet conditions is analyzed. When the source term F is a linear function, the problem is explicitly solved by means of a Fourier series with properties of rapid convergence. When F is nonlinear, appropriate estimates of this series allow to deduce a priori estimates, continuous dependence and asymptotic behaviour of the solution.

On Exponentially Shaped Josephson Junctions

The paper deals with a semilinear integrodifferential equation that characterizes several dissipative models of Viscoelasticity, Biology and Superconductivity. The initial - boundary problem with Neumann conditions is analyzed. When the source term F is a linear function, then the explicit solution is obtained. When F is non linear, some results on existence, uniqueness and a priori estimates are deduced. As example of physical model the reaction - diffusion system of Fitzhugh Nagumo is considered.

On a Model of Superconductivity and Biology

A superconductive model characterized by a third order parabolic operator $ {\mathcal L}_\varepsilon $ is analyzed. When the viscous terms, represented by higher-order derivatives, tend to zero, a hyperbolic operator $ {\mathcal L}_0 $ appears. Furthermore, if
${\mathcal P}_\varepsilon$ is the Dirichlet initial-boundary value problem for $ {\mathcal L}_\varepsilon$,
when ${\mathcal L}
_\varepsilon $ turns into ${\mathcal
L}_0 , $
 ${\mathcal P}_\varepsilon$ turns into a problem ${\mathcal P}_0$ with the same initial-boundary conditions of
${\mathcal P}_\varepsilon $.
As long as the higher-order derivatives of the solution of ${\mathcal P}_0$ are bounded, an estimate of solution for the nonlinear problem related to the remainder term $ r, $ is achieved. Moreover, some classes of explicit solutions related to $ {\mathcal P}_0 $ are determined, proving the existence of at least one motion whose derivatives are bounded. The estimate shows that the diffusion effects are bounded even when time tends to infinity.

Monica De Angelis

Papers

Existence, uniqueness and a priori estimates for a nonlinear integro-differential equation

Existence and uniqueness of solutions of a class of third order dissipative problems with various boundary conditions describing the Josephson effect

On Exponentially Shaped Josephson Junctions

On a Model of Superconductivity and Biology

Diffusion effects in a superconductive model