PDE: first quadrant robin wave equation - homogenous

HALEY PHAM

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Jun 22, 2022
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I started by solving like I would do with any wave equation but couldn't understand how to incorporate the Robin IC.
got stuck!
could really use your help!
 

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Subhotosh Khan

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I started by solving like I would do with any wave equation but couldn't understand how to incorporate the Robin IC.
got stuck!
could really use your help!
1655937515145.png

This almost looks like equation of heat transfer in a plate. I have NOT solved this problem - but I would start with the assumption:

u (x, t) = P(x) * Q(t)

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 

HALEY PHAM

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Joined
Jun 22, 2022
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I happened to forget to add the c^2 in the first equation indicating this is in fact a wave equation.
I started by solving like I would do with any wave equation (and got to the left and right mover F(x), G(x) - am I supposed to sum them and get the d'Alembert formula?)
but couldn't understand how to incorporate the Robin boundary conditions.
 

Subhotosh Khan

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Staff member
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I happened to forget to add the c^2 in the first equation indicating this is in fact a wave equation.

So post the corrected equation after inserting c^2.

I started by solving like I would do with any wave equation (and got to the left and right mover F(x), G(x) - am I supposed to sum them and get the d'Alembert formula?)

Please share your work - as far as you have progressed.
 

nasi112

Full Member
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Aug 23, 2020
Messages
560
The OP meant to write
\(\displaystyle u_{tt} - c^2u_{xx} = 0\)

Let the general solution be
\(\displaystyle u(x,t) = \phi(x + ct) + \psi(x - ct)\)

Now satisfy the first initial condition. What do you get?

Hint:
The final solution has two conditions: \(\displaystyle x > ct \) and \(\displaystyle x < ct\).
 
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