question archive 1) Let = [0; a] £ [0; b] ½ R2
1) Let = [0; a] £ [0; b] ½ R2
Subject:StatisticsPrice: Bought3
1) Let = [0; a] £ [0; b] ½ R2. We seek the (unique) solution u : ! R to the Laplace boundary-value problem
¢u = 0 in ;
u(0; y) = u(x; 0) = 0; for 0 · x · a; 0 · y · b;
ux(a; y) = 0; for 0 · y · b;
u(x; b) = g(x); for 0 · x · a;
where g : [0; a] ! R is a known function. Using the method of separation of variables, calculate
the solution up to unknown constants, and give a condition that can enable us to calculate these
unknown constants.
