For a linear transport equation in one space dimension with speeds in a compact interval and a general symmetric kernel for the change of velocity a problem with free boundary (Stefan problem) is stated. The case of constant speed corresponds to a Stefan problem for the damped wave equation (telegraphers equation). Existence and uniqueness of the free boundary is shown, and the connection to th...

We consider a coupled PDE system arising in noise reduction problems. In a two dimensional chamber, the acoustic pressure (unwanted noise) is represented by a hyperbolic wave equation. The floor of the chamber is subject to the action of piezo-ceramic patches (smart materials). The goal is to reduce the acoustic pressure by means of the vibrations of the floor which is modelled by a hyperbolic ...

We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with zero speed of propagation with exactly the same profile as the original one. This procedure allows us to compute simultaneously th...

A recent development of a parabolic equation method for wave propagation in a non-orthogonal coordinate system is reviewed. A transformation of the full governing equation prior to development of any approximation leads to a model whose results stand in closer agreement to laboratory data for a case of waves propagating into a breakwater harbor. The effect of amplitude dispersion on predicted w...

The propagation of linear water waves over a three-dimensional ocean is modelled using the mildslope equation. Various parabolic wave models are described that approximate the governing elliptic partial differential equation, and so are very convenient for computing wave propagation over large distances. Several aspects are discussed: computation of the reflected wavefield, the construction of ...

it is well known that the parabolic partial differential equationsin two or more space dimensions with overspecified boundary data,feature in the mathematical modeling of many phenomena. in thisarticle, an inverse problem of determining an unknowntime-dependent source term of a parabolic equation in generaldimensions is considered. employing some transformations, wechange the inverse problem to...

We apply functional analytical and variational methods in order to study well-posedness and qualitative properties of evolution equations on product Hilbert spaces. To this aim we introduce an algebraic formalism for matrices of sesquilinear mappings. We apply our results to parabolic problems of different nature: a coupled diffusive system arising in neurobiology, a strongly damped wave equati...