This work considers the formulation and solution of the Dirichletproblem 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 ofa series of spherical functions, and the coefficients of the series are determined from the boundary conditions.The properties of the solution are proven: smoothness inside and on the surface of the sphere, uniqueness of the solution of the Dirichlet problem on the sphere. The physical interpretation of the obtained solution is given, which can describe various physical processes, such as the distribution of potential or temperature.The work is of interest to specialists in the field of mathematical physics, the theory of partial differential equations, as well as to researchers engaged in physical modeling processes in spherical domains.
This work considers the formulation and solution of the Dirichletproblem 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 ofa series of spherical functions, and the coefficients of the series are determined from the boundary conditions.The properties of the solution are proven: smoothness inside and on the surface of the sphere, uniqueness of the solution of the Dirichlet problem on the sphere. The physical interpretation of the obtained solution is given, which can describe various physical processes, such as the distribution of potential or temperature.The work is of interest to specialists in the field of mathematical physics, the theory of partial differential equations, as well as to researchers engaged in physical modeling processes in spherical domains.
| № | Имя автора | Должность | Наименование организации |
|---|---|---|---|
| 1 | Bogdan . . | Student | Fergana State University |
| № | Название ссылки |
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