I have to find the solution to this problem:

where f(x,t) is a step function:

for and

else

I know I have to use the duhamel's principle, but I have problem with the integration of f(x,t).

Can anybody help me please?

thank you

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- Mar 12th 2010, 02:17 PMsidiwave equation
I have to find the solution to this problem:

where f(x,t) is a step function:

for and

else

I know I have to use the duhamel's principle, but I have problem with the integration of f(x,t).

Can anybody help me please?

thank you - Mar 12th 2010, 09:02 PMTheEmptySet
So using Duhammel's principle you need to find a

Such that with initial conditions

Now by D'lamberts we know that

Now by Duhammel's principle the solution is

Note that the region of integration depends on the x and t varaibles. Also the forcing function is non zero in the rectangle (In red in the diagram). In this diagram the function will be zero in any of the shaded (blue) area's and the wave will travel in the white strips.. I hope this helps.

Attachment 15879 - Mar 13th 2010, 01:28 AMsidi
I still don't know how to find the region of integration....

On your diagram are there the x and t axis? Where is s?