Heat equation with annoying source term

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SUMMARY

The discussion centers on solving the heat equation with a specific source term represented as ∂u/∂t + ∂²u/∂x² = So*δ(x-xo)*sin(wo*t). The participant expresses difficulty in applying the separation of variables method due to the complexity introduced by the cyclic source. A recommended resource is the book "Conduction of Heat in Solids" by Carslaw and Jaeger, which is noted as a comprehensive guide for understanding the heat equation.

PREREQUISITES
  • Understanding of partial differential equations (PDEs)
  • Familiarity with the heat equation and its applications
  • Knowledge of the separation of variables technique
  • Basic concepts of delta functions and cyclic sources
NEXT STEPS
  • Study the method of Green's functions for solving PDEs
  • Explore the application of Fourier series in heat equation problems
  • Read "Conduction of Heat in Solids" by Carslaw and Jaeger
  • Investigate numerical methods for solving PDEs with source terms
USEFUL FOR

Mathematicians, physicists, and engineers dealing with heat transfer problems, particularly those interested in advanced methods for solving partial differential equations with complex source terms.

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.
 

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