Все науки. №12, 2024. Международный научный журнал - страница 5

Where, the coefficient of energy conductivity is determined in (20), along with all the determined parameters, including the coefficients of energy conductivity of the vacuum between the Sun and the Earth (21), the specific energy capacity (22) and the available energy density under the circumstances in the specified area (23).

Based on the calculated parameters according to (21—23), expression (20) obtains a numerical indicator (24).

Based on the conditions obtained, it is possible to determine that the problem can be solved by taking the form of an equation of the form (25), where, after substitution, a transformation can be obtained according to (26), with an equated coefficient (27).

From expression (27), 2 partial differential equations are formed – 1 ordinary with respect to time in the first degree and the second in the square of partial derivatives. The first equation is solved by adopting a general solution with an exponential form, where, after substitution, a characteristic form is presented, from which a general form of the function is formed – the solution of the resulting ordinary differential equation in time (28).

With respect to time, initial conditions (3—4) have already been obtained, which can be substituted to form initially the coefficient value from (27) to (29), the independent variable in (30) and the resulting form of a function with known constants in (31).

The resulting function is the solution of only one differential equation, the second (32) is formed relative to the Laplacian in a spherical coordinate system with a known constant.

The solution of this equation is presented initially after the disclosure of the Laplacian for the Ψ-function in a spherical coordinate system, where the Fourier variable separation method is applied, which was originally applied in (26). Then subsequently, after substitution, the resulting separation expression is revealed, forming separate groups of derivatives in the specified system (33).

Taking into account the resulting transformation and taking into account the transformation of the original ratio, the Laplacian ratio of the function and the function itself can be substituted into the transformed form after separating the variables, from which a separate additional ratio is created for each function – radius, first and second angles, as well as for the second derivatives of these expressions (34).