Let

a) Prove that μ satisfies the heat equation (i.e., μxx - μt = 0 for all t > 0 and x ˆˆ R).
b) If a > 0, prove that u(x, t) †’ 0, as t †’ 0+, uniformly for x ˆˆ [a, ˆž).

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u(x, t) =- 4st t