Mathematics – Analysis of PDEs

Scientific paper

[
0.00
] – not rated yet
Voters
0
Comments 0

2008-12-09

Mathematics

Analysis of PDEs

17 pages, 3 figures. Minor adjustments made to the introduction

Scientific paper

We study the Cauchy problem associated with the equations governing a fluid loaded plate formulated on either the line or the half-line. We show that in both cases the problem can be solved by employing the unified approach to boundary value problems introduced by on of the authors in the late 1990s. The problem on the full line was analysed by Crighton et. al. using a combination of Laplace and Fourier transforms. The new approach avoids the technical difficulty of the a priori assumption that the amplitude of the plate is in $L^1_{dt}(R^+)$ and furthermore yields a simpler solution representation which immediately implies the problem is well-posed. For the problem on the half-line, a similar analysis yields a solution representation, but this formula involves two unknown functions. The main difficulty with the half-line problem is the characterisation of these two functions. By employing the so-called global relation, we show that the two functions can be obtained via the solution of a complex valued integral equation of the convolution type. This equation can be solved in closed form using the Laplace transform. By prescribing the initial data $\eta_0$ to be in $H^3(R^+)$, we show that the solution depends continuously on the initial data, and hence, the problem is well-posed.

**Ashton Anthony C. L.**

Mathematics – Analysis of PDEs

Scientist

**Fokas Athanassios S.**

Physics – Condensed Matter – Statistical Mechanics

Scientist

No associations

LandOfFree

If you have personal experience with

A Novel Method of Solution for the Fluid Loaded Platedoes not yet have a rating. At this time, there are no reviews or comments for this scientific paper.A Novel Method of Solution for the Fluid Loaded Plate, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A Novel Method of Solution for the Fluid Loaded Plate will most certainly appreciate the feedback.

Profile ID: LFWR-SCP-O-282141

Use Google custom search:

All data on this website is collected from public sources.
Our data reflects the most accurate information available at the time of publication.