This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ﬁnd 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...
View
Full Document
 Spring '07
 Trangenstein
 Equations, Boundary value problem, Partial differential equation, PRTL DIFF, PRTL DIFF EQUATIONSMATH, Stefano Guerra, PRTL DIFF EQUATIONS

Click to edit the document details