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Consider the problem $$\begin{cases}u_{tt}=u_{xx}-2au_{x}+a^{2}u, (x,t)\in\mathbb{R}^{2}\\[8pt] u(x,0)=f(x), x\in\mathbb{R}\\[8pt] u_{t}(x,0)=g(x), x\in\mathbb{R} \end{cases}$$ where $a>0$.

(a)Study the existence and uniqueness of local solutions analytical of the problem, assuming $f$ and $g$ analytic in a neighborhood of $(0,0)$.

(b)Assuming $f\in C^{2}(\mathbb{R}), g\in C^{1}(\mathbb{R})$, show that there exists a unique solution of the problem in $C^{2}(\mathbb{R})$ and display such solution.

Michael Hardy
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Manoel
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  • I see this is your seventh question here and yet you've accepted only one answer so far. If you get a satisfying answer, please accept your favorite one. – Git Gud Feb 05 '13 at 20:02
  • What's wrong with my question? Why did I receive $-1$? – Manoel Feb 05 '13 at 20:53
  • I didn't downvote you, it was someone else. – Git Gud Feb 05 '13 at 21:01
  • I did not downvote either but I can see NO personal thought or comment in this question. This is bad practice since (1) it makes difficult to adjust an answer suited to the level of your understanding, and (2) one could imagine that you are simply dumping your homework on the site and waiting for a full proof to appear to put your name on it and hand it back. – Did Feb 05 '13 at 21:17
  • Who gives downvote in question could say why, can help the questioner! Simply give downvote, can take on all questions. – Manoel Feb 06 '13 at 14:28
  • @GitGud you could see that I gave answers that were ignored (http://math.stackexchange.com/questions/261574/a-particular-way-of-write-a-polynomial/261851#261851 and http://math.stackexchange.com/questions/257116/pullback-of-1-form/257137#257137;. Then you also manifest on them! – Manoel Feb 07 '13 at 01:49
  • @Did, have you seen my questions here on the site? In most, there are my comments. So please, do not talk without knowing.This answers (1). For (2), have you ever thought that most of the issues here can interpretadas so, but not necessarily. – Manoel Feb 07 '13 at 01:51
  • Thanks for the answer. I am afraid that the way you asked your other questions is off-topic, hence (1) and (2) fully apply. The last sentence of your comment is not very clear but if you mean that many questions on the site are poorly asked, I agree. If you mean that (1) and (2) apply to most questions on the site, I disagree. Many questions are following the advice given about how to ask. Unfortunately, yours does not, but nothing prevents you to remedy to this NOW on THIS question. – Did Feb 07 '13 at 09:34
  • OK, now I checked: NONE of your questions on the site has ANY personal input. – Did Feb 07 '13 at 09:37

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