2. Laplace equation (Haberman § 2.5)

Consider

8² u 8² u

+

əx²

Əy²

u(0, y)

u(x, 0)

u(1, y)

=

0 (0

0, u(x, 3) = 0

20 sin(x)

30 sin(Ty/3)

(6)

(8)

(9)

that describes the steady state temperature distribution in a rectangle subject to Dirichlet

boundary conditions.

(a) Using separation of variables, solve (6)-(9) for u(x, y).

(b) Use Matlab to plot the isotherms (lines of constant u) for your solution in (a). See

laplaccexallS23.m on Canvas for the example from lecture.

(c) Briefly discuss your solution in the context of the maximum/minimum principle of the

Laplace equation.