APM346-2012 > Home Assignment 3

Problem 4

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Vitaly Shemet:
Is initial Gaussian centered at $0$? Considering opposite I'm getting $M(T)$ and $m(T)$  neither increasing nor decreasing, what seems suspicious to me. If it is centered then $M(T)$ is decreasing... In other words, is $u(0,0)$ or $u(l,0) = max    u(x,t)$ for all $x$

Victor Ivrii:
You need to find minima and maxima. Where they are located? -- you need to find this.

Thomas Nutz:
I don't think that the maximum in the region $0\leq x \leq l$, $0 \leq t \leq T$ must either decreases or increase; I think it also can stay constant (e.g. iron rod that is initially very hot in the middle, then the maximum is found at t=0, x=l/2) and M(T) =const.

Am I wrong?

Victor Ivrii:

--- Quote from: Thomas Nutz on October 08, 2012, 03:53:35 PM ---I don't think that the maximum in the region $0\leq x \leq l$, $0 \leq t \leq T$ must either decreases or increase; I think it also can stay constant (e.g. iron rod that is initially very hot in the middle, then the maximum is found at t=0, x=l/2) and M(T) =const.

Am I wrong?

--- End quote ---

You are definitely correct. Since domain increases as $T,L$ grow, then maximum could only increase (or stay the same) and minimum could only decrease (or stay the same). The question is, what happens in the framework of the given problem

Jinlong Fu:
q4

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