Unformatted text preview: ∂x (0 ,t ) = 1 ∂u ∂x ( L,t ) = β Make sure you can explain what it means for a problem to be well-posed. 3. What is the compatibility condition for Laplace’s equation in three dimensions with heat ﬂow given on the boundaries (note that Ω denotes the domain, and δ Ω denotes the bound-ary of the domain): ∇ 2 u ( x ) = 0 ∀ x ∈ Ω-c ∇ u · ˆn | δ Ω = g ( x ) BONUS! (don’t spend too much time on this © ) Prove that all positive even integers ≥ 4 can be expressed as the sum of two primes (Strong Goldbach Conjecture) Written by Anil Damle and Anna Lieb 1 revised September 2010...
View Full Document
- Fall '08
- Laplace, Boundary value problem, Prime number, Strong Goldbach Conjecture