SOLUTION OF THE DIRICHLET PROBLEM ON A SPHERE FOR THE LAPLACE EQUATION
Ключевые слова:
Laplace's equation, mathematical physics, Dirichlet problem, spherical geometry, electrostatics, gravity, heat transfer, temperature distribution, distribution of electric charges, gravitational potentials, modeling of physical phenomena, practical application, solution methods, properties of solutions.Аннотация
This work considers the formulation and solution of the Dirichlet problem on a sphere. The domain of the problem is a sphere, and the boundary conditions are given on its surface. The solution is presented in spherical coordinates using the method of separation of variables. A general solution is obtained in the form of a series of spherical functions, and the coefficients of the series are determined from the boundary conditions.
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