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 wellposed. 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 boundary of the domain): ∇ 2 u ( x ) = 0 ∀ x ∈ Ωc ∇ 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...
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 Fall '08
 ABLOWITZ
 Laplace, Boundary value problem, Prime number, Strong Goldbach Conjecture

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