MHB Heat equation with annoying source term

tylerbizoff
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Hello to everyone,

I urgently need to solve the following pde: ∂u/∂t +∂²u/∂x² = So*δ(x-xo)*sin(wo*t)

It's the heat equation with a cyclic source. The lentgh of the cable is L.

I have no clue how to do this with such a source, all i have learned was to do a separation of variables, but it does not seem to work in my case.

Anybody can help or has an interesting link for me?
 
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Well, I'm not sure I can help out immediately. However, Carslaw and Jaeger is the standard, comprehensive book on the heat equation, and would be the most likely book to help you out. Check to see if your school's library has it.
 

Thread 'A question about variables of integration'

I have the equation ##F^x=m\frac {d}{dt}(\gamma v^x)##, where ##\gamma## is the Lorentz factor, and ##x## is a superscript, not an exponent. In my textbook the solution is given as ##\frac {F^x}{m}t=\frac {v^x}{\sqrt {1-v^{x^2}/c^2}}##. What bothers me is, when I separate the variables I get ##\frac {F^x}{m}dt=d(\gamma v^x)##. Can I simply consider ##d(\gamma v^x)## the variable of integration without any further considerations? Can I simply make the substitution ##\gamma v^x = u## and then...
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