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Unformatted text preview: , u ( r, , , 0) = f ( r, , ) u t ( r, , , 0) = 0 . 5.- (25 pts) (a) (15 pts) Solve 2 u = 0 for < 1 , t > , u = g ( , ) for = 1 where the function g is assumed to satisfy Z 2 Z g ( , ) sin( ) dd = 0 . (1) Show that this problem admits a unique solution up to an additive constant, that can be determined if, for example, we assume the temperature scale is such that u = 0 at = 0 for t = 0. (b) (10 pts) What happens if the integral in (1) is not zero? Compare with problem 1.: no special conditions on the boundary values were needed there. Explain! Due April 30, 3:00pm....
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This note was uploaded on 01/08/2011 for the course ACM 95c taught by Professor Nilesa.pierce during the Spring '09 term at Caltech.
- Spring '09