Файл	Ном	Сабт карда шуд
Kiboriyon Bobojon Kiborzoda	THE SOLVABILITY OF BOUNDARY VALUE PROBLEMS IN ELECTRODYNAMICS NON-LINEAR MEMORY	14

Authors: Kiboriyon Bobojon Kiborzoda - Candidate of Physics and Mathematics, Senior Lecturer of the Department of Information Technology and Methods of Teaching Informatics, Nosir Khusrav Bokhtar State University

JOURNAL NUMBER: 3(58). YEAR OF ISSUE: 2021. LANGUAGE OF THE ARTICLE: Russian

ANNOTATION

Initially, a lemma was proved in the paper that for-positive constants, is a continuous and positive function having continuous positive derivatives of the first order for and, in addition, for

then for the above mentioned boundary value problem the a priori estimate    ,where ĉ₁,  ĉ₂, с - is determined by the data of the problem: ѱ(0),  and the domain Ω.

To prove the lemma, we use the nonlinear Granwall - Belmann inequalities. Also given by a generalized solution of the above specified system satisfying the boundary and initial conditions. In the course of solving the problems, approximate solutions were used

(t) =

(t) =

where   is defined from the equation itself. To determine   - given the initial conditions

 in   as n → ∞,

    in   as n → ∞.

This theorem proves the boundedness

H_n   в 

E_{n    в} 

Thus, the existence and boundedness of solutions are proved.

KEY WORDS

theorem, vector functions, a priori estimate, initial conditions boundary value problems, constituent equations, generalized solutions, nonlinear Granwall - Belmann inequalities.

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