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.
| № | Author name | position | Name of organisation |
|---|---|---|---|
| 1 | Bogdan . . | Student | Fergana State University |
| № | Name of reference |
|---|---|
| 1 | 1.Kirsanov M.N. Maple 13 and Maplet. Solving mechanics problems. M.: Fizmatlit, 2010, 349 p.2.GaltsovD.V. Theoretical physics for mathematics students. –M.: Publishing house Mosk. University, 2003. –318 p.3.Ignatiev Yu.G. Mathematical and computer modeling of fundamental objects and phenomena in the Maple computer mathematics system. Lectures for schoolon mathematical modeling. / Kazan: Kazan University, 2014. -298 p.4.Matrosov A.V. Maple 6. Solving problems of higher mathematics and mechanics. –St. Petersburg: BHV-Petersburg. –2001.–528 p.5.Samarsky A. A., MikhailovA. P. Mathematical modeling: Ideas. Methods. Examples. —2nd ed., rev. -M.: Fizmatlit, 2005. -320 p.6.Matrosov A.V. Maple 6. Solving problems of higher mathematics and mechanics. –St. Petersburg: BHV-Petersburg, 2001, 528 p.7.N. Teshavoeva. Mathematicianphysics methodology. Fergana. Ukituvchi. 1980.8.M. Salokhiddinov. Mathematician physics tenglamalari. Tashkent. Uzbekistan. 2002.9.M. T. Rabbimov. Mathematics. Tashkent. Fan ziyoshi. 2022. –285 p.10.Lebedev N.N., Skalskaya I.P., Uflyand Y.S. Collection of problems in mathematical physics. -M.: Gostekhizdat, 1955.11.Smirnov M.M. Problems on the equations of mathematical physics. -M.: Nauka, 197512.Tikhonov A.N., Samarsky A.A. Equations of mathematical physics. -M.: MSU, Science, 2004. |