Calculation of Green's function for Poisson's equation on a semi-disk using a Fourier transform in the radial variable
Palavras-chave:Green's function, Poisson, semi-disk, radial, Fourier transform
A new calculation of Green's function for the problem with Poisson's equation on a semi-disk under mixed Dirichlet-Neumann boundary conditions is presented. The method consists in first (a) employing a Fourier transform in the radial variable to calculate the solution of the simpler problem that is obtained with the homogenization of the boundary conditions, and then (b) inferring the desired Green's function by comparing the expression of this calculated solution with the one given by Green's formula. The solution that the method yields is elaborated to the point of having the same closed form that the method of images provides.
R. T. Couto. A equação de Laplace num semidisco sob a condição de fronteira mista DirichletNeumann. In: Proceeding Series of the Brazilian Society of Computational and Applied Mathematics. 2021, pp. 01034117. doi: 10.5540/03.2021.008.01.0341.
J. D Jackson. Classical Electrodynamics. 2nd ed. New York: John Wiley & Sons, 1975. isbn: 0-471-43132-X.
E. Butkov. Mathematical Physics. Reading, MA: Addison-Wesley, 1973.
F. B. Hildebrand. Advanced Calculus for Applications. 2nd ed. Englewood Clis, NJ: Prentice-Hall, 1976. isbn: 0-13-011189-9.
Fritz John. Partial Diferential Equations. 4th ed. New York: Springer-Verlag, 1982. isbn: 0-387-90609-6.