| University | Singapore Management University (SMU) |
| Subject | Partial Differential Equations |
Assignment Details:
Steady-state heat conduction in a region indicates an equilibrium temperature within that region.
1. Consider the steady-state heat equation
2. Show that the steady-state heat equation (PE1) with nonhomogenous boundary conditions
u(0)=∝, u(L)=β
has, using (L1g), solution
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3. Consider a rectangular region Ω = [0, L] × [0, H]: the equilibrium temperature u(x, y) satisfies Laplace’s equation
Find a solution u(x, y) to (LE) under (LER). (10)
4. Consider a rectangular region Ω: the equilibrium temperature satisfies Poisson’s equation
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