Nonlinear conservation laws with moving boundaries often arise in applications such as gas and plasma dynamics and more recently in the context of nuclear fusion reactors. Gaining insight into the nature of solutions to such models and their dependence upon design parameters is often done numerically. Instead of relying upon numerics, in this paper we use formal asymptotics to study a model of ...

The diffraction of electromagnetic and light waves by an aperture in a plane conducting screen is a classical boundary value problem. As is well known, theoretical analysis aims at a solution of the vector Maxwell equations, which incorporates a prescribed form of excitation and satisfies appropriate boundary conditions on the screen and in the aperture. A small measure of progress towards this...

As Henri PoincarC once remarked, “solution of a mathematical problem” is a phrase of indefinite meaning. Pure mathematicians sometimes are satisfied with showing that the non-existence of a solution implies a logical contradiction, while engineers might consider a numerical result as thc only reasonable goal. Such one sided views seem to reflect human limitations rather than objective values. I...