Boundary Value Problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg102231] Boundary Value Problem*From*: dimitris <dimmechan at yahoo.com>*Date*: Sun, 2 Aug 2009 05:57:42 -0400 (EDT)

Hello to all. I have the following BVP, consisting of the equations eq1 = (1 - a^2)*D[f[x, y], {x, 2}] + D[f[x, y], {y, 2}] == 0; eq2 = (1 - b^2)*D[g[x, y], {x, 2}] + D[g[x, y], {y, 2}] == 0; and the boundary conditions bc1 = (b^2 - 2)*D[f[x, y], {x, 2}] - 2*D[g[x, y], {x, 1}, {y, 1}] == (- P)*DiracDelta[x]; bc2 = (b^2 - 2)*D[g[x, y], {x, 2}] + 2*D[f[x, y], {x, 1}, {y, 1}] == 0; where P a constant. The problem describes the response of an elastic isotropic linear half plane to the steady state motion of a concentrated normal load at the surface. (The so called Cole-Huth problem). a and b are the Mach numbers. Three cases can be distinguished: a>b>1 (supersonic case) a>1>b (transonic case) 1>a>b (subsonic case) There a couple of solutions in the literature. One such is, integral transform analysis. In fact, I have solved it with the aim of Laplace transform. But I wonder if (and of course how!) Mathematica can be utilized to solve above BVP. Thank you very much in advance