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Unformatted text preview: 7. Boas, Chapter 13, Section 7, Problem 18 1 8. In class, we found that in the case of diusion, if at t=0 we have u ( x,y,t = 0) = ( x-x ) ( y-y ), the subsequent distribution is given by the Green function G ( x,x ,y,y ; t ) = 1 4 2 t e-( x-x ) 2 +( y-y ) 2 4 2 t At t = 0, we place a point source in the rst quadrant at x = a and y = b (where a &gt; 0 and b &gt; 0). We also have boundary conditions u x = 0 for x = 0, and u = 0 for y = 0. Using the image method and the Green function given above, determine the distribution u ( x,y,t ) in the rst quadrant ( x &gt; 0 and y &gt; 0). Sketch the source and the images, using plus sign for sources and minus signs for any sinks. 2...
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- Spring '03
- Boundary value problem, Boundary conditions, ﬁrst quadrant, Green function