Partial Differential Equation is: $$\frac{∂u}{∂t} = \frac{∂^2u}{∂x^2}$$

Where $t>0$, and $0<x<1$.

With the boundary conditions:

$$u(0,t)=1$$ $$u(1,t) = 1$$

and the initial conditions:

$$u(x,0) = 1+\sin{(πx)}$$

I'm trying to solve this by using Laplace transform but I couldn't.


1 Answer 1


You haven't even bothered to ask a question. Good effort.

Here is a list of examples for your problem. Example 3 is something very similar to what you are trying to do. If I was you - Be able to understand all three examples before trying the one you've posted, otherwise you won't get it. Good Luck! Post your attempts if you get stuck and we can help.

  • $\begingroup$ Now it looks better $\endgroup$
    – M.dogan
    Jan 7, 2017 at 11:48
  • $\begingroup$ Have you ever done any similar examples? What have you attempted thus far? If I defined $\mathcal{L}$ as the Laplace operator, would you know what $\mathcal{L(\frac{\partial u}{\partial t})}$ was? $\endgroup$ Jan 7, 2017 at 11:49
  • $\begingroup$ Actually I don't have any similar examples and Also I looked some "advanced engineering math" lecture book but I couldn't find $\endgroup$
    – M.dogan
    Jan 7, 2017 at 11:52
  • $\begingroup$ Thank you so much @Rumplestillskin $\endgroup$
    – M.dogan
    Jan 7, 2017 at 12:11
  • $\begingroup$ @M.dogan All G. If it's what you're looking for then kindly accept the answer so people know you're all set! Example 3 is almost identical to your problem so you should be sweet. $\endgroup$ Jan 7, 2017 at 12:15

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