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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
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