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### Messages - Levon Avanesyan

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##### Home Assignment 5 / Problem 1
« on: October 29, 2012, 12:14:01 PM »
In C part, shouldn't it be sinh(Î·x) instead of sin(Î·x)?

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##### Misc Math / Re: TT1Problem6
« on: October 15, 2012, 02:15:11 PM »
So, first start with whole interval and then as before examples, make it in the 0<x<+âˆž; Right?
I think so

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##### Misc Math / Re: TT1Problem6
« on: October 15, 2012, 01:47:38 PM »
I guess yous should apply the method of continuation here.

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##### Home Assignment X / Re: problem 3
« on: October 15, 2012, 01:12:07 PM »
Thanks for your help Prof. Ivrii

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##### Home Assignment X / Re: problem 3
« on: October 15, 2012, 12:59:39 PM »
Just have edited the original post

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##### Home Assignment X / Re: problem 3
« on: October 15, 2012, 12:44:45 PM »
by sqr I mean "to the power of 2".

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##### Home Assignment X / Re: problem 3
« on: October 15, 2012, 12:40:31 AM »
So, after some more time spent on this problem as a result of integration I get
$$\Re(\beta(|u_t|^2))(x=L) - \Re(\alpha(|u_t|^2))(x=0).$$
Does this imply that the answers should be

a) $\Re(\alpha)=0, \Re(\beta)=0$
b) $\Re(\alpha)>0, \Re(\beta)<0$

P.S. Zarak, Thanks for editing!

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##### Home Assignment X / Re: problem 3
« on: October 14, 2012, 07:42:16 PM »
Here are the answers I got.
a) $alpha$ = $beta$
b) $beta$ < $alpha$
Are they correct Prof. Ivrii?

P.S. Dont post the solution because a) dont know how to type math, b) dont have a scanner  c) it is written in a very messy style

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##### Home Assignment 3 / Re: Problem 6
« on: October 11, 2012, 01:21:49 PM »
Question: is in (c) $u(x,t)=c$ is a solution for any constant $c$?
No. From Robin conditions we can see that  $u(x,t)=c$ is a solution only when $c=0$.

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##### Home Assignment 3 / Re: Problem5
« on: October 09, 2012, 01:02:49 PM »
Maximum principle states that U(x,t) takes maximum values only when at least one of the following holds: t=0 or x=0 or x=L. So your aim is to find where U(x,t) is at maximum. After you find the maximum point you will see that smth is wrong

You are formulating a more demanding problem.

Sorry, I was sleepy while writing that
EDIT
After rereading the problem 5, I noticed that part b straightly asks us to find the maximum point, so I guess I am was not stating a more demanding problem...

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##### Home Assignment 3 / Re: Problem5
« on: October 09, 2012, 01:49:02 AM »
Maximum principle states that U(x,t) takes maximum values only when at least one of the following holds: t=0 or x=0 or x=L. So your aim is to find where U(x,t) is at maximum. After you find the maximum point you will see that smth is wrong

P.S. When the author asks "where precisely the proof of maximum principle breaks down", he means that there is a standard way to prove the maximum principle for heat equation. And the question is "At which step exactly, having this equation, we cannot continue moving, while we could have continued moving if we had heat equation.

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##### Home Assignment 3 / Re: Problem 2
« on: October 06, 2012, 02:37:19 PM »
In this problem it is stated that we should use formulas (1)-(2). But shouldn't we have an initial condition in order to apply these formulas.

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##### Home Assignment 1 / Re: Problem 5
« on: September 23, 2012, 02:51:20 AM »
I will expand this question a little bit:
So, can we use the formula of general solution for wave equation or we should prove/derive it?

P.S. This is my first post here, so I am not sure if I am asking an appropriate question

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