Finding Green's Function for Half Space Neumann Problem

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SUMMARY

The discussion focuses on finding the Green's function for the half space Neumann problem defined in the domain z>0, specifically addressing the Laplacian equation with boundary conditions. Key methods highlighted include the method of images, Fourier transform techniques, and separation of variables. Each method provides a systematic approach to derive the Green's function while adhering to the specified boundary conditions. The importance of selecting the appropriate technique based on the problem's requirements is emphasized for effective problem-solving.

PREREQUISITES
  • Understanding of Green's functions in partial differential equations
  • Familiarity with Neumann boundary conditions
  • Knowledge of Fourier transforms and integral equations
  • Proficiency in separation of variables technique
NEXT STEPS
  • Study the method of images for solving boundary value problems
  • Learn about Fourier transform applications in solving partial differential equations
  • Explore integral equations and their solutions in mathematical physics
  • Investigate series solutions using the separation of variables method
USEFUL FOR

Mathematicians, physicists, and engineers working on boundary value problems, particularly those dealing with partial differential equations and Green's functions in applied mathematics.

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Hi all...need a little help with this one...

I need to find the Green's function for the half space Neumann problem in the domain z>0. i.e. Laplacian u=f in D, du/dn=h on the boundary of D.

Any ideas?
 
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ya of corse
you can see http://www.ma3n.org/pages/jazar/
and problemes elliptiques
 
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Thanks!

Finding the Green's function for the half space Neumann problem can be a challenging task, but there are a few approaches you can take to solve it. One method is to use the method of images, where you create a mirror image of the problem in the lower half space and use the reflection principle to find the solution. Another approach is to use the Fourier transform to convert the problem into an integral equation, and then solve for the Green's function using this equation. Additionally, you can also use the method of separation of variables to find the Green's function in terms of a series solution. Whichever method you choose, it is important to carefully consider the boundary conditions and use appropriate techniques to solve for the Green's function. I hope this helps and good luck with your problem!
 

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