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Unformatted text preview: u xx10 xu + x = u t t > 0 0 x 1 u (0 ,t ) = u (1 ,t ) t > u x (0 ,t ) = u x (1 ,t ) t > u ( x, 0) = x 2 (3) (a) Use separation of variables to nd the boundary value problem that the function X ( x ) has to solve in order for u ( x,t ) = X ( x ) T ( t ) to be a nonzero solution of the homogenous boundary problem associated to the equation above. 5 (b) Is the boundary problem you found selfadjoint? Justify yout answer. 6 4. Find the solution of the Laplace equation: u xx + u yy = 0 x a y b u ( x, 0) = 0 x a u ( x,b ) = f ( x ) 0 x a u (0 ,y ) = 0 y b u ( a,y ) = g ( y ) 0 y b (4) 7...
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 Spring '07
 Trangenstein
 Equations

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