UNIFORM ESTIMATES FOR SOLUTIONS OF A CLASS OF NONLINEAR EQUATIONS IN A FINITE-DIMENSIONAL SPACE

Koshanov B.D. Bakytbek M.B. Koshanova G.D. Kozhobekova P.Zh. Sabirzhanov M.T.
31 December 2023 al-Farabi Kazakh State National University

KazNU Bulletin. Mathematics, Mechanics, Computer Science Series
2023 #120 Issue 4 16 - 23 pp.

The need to study boundary value problems for elliptic parabolic equations is dictated by numerous practical applications in the theoretical study of the processes of hydrodynamics, electrostatics, mechanics, heat conduction, elasticity theory, quantum physics. Let H (dimH ≥ 1) – a finite-dimensional real Hilbert space with inner product 〈·, ·〉 and norm ‖ · ‖. We will study the equation of the following form u + L (u) = g ∈ H, where L(·) is a non-linear continuous transformation, g is an element of the space H, u is the required solution of the problem from H. In this paper, we obtain two theorems on a priori estimates for solutions of nonlinear equations in a finite-dimensional Hilbert space. The work consists of four items. The conditions of the theorems are such that they can be used in the study of a certain class of initial-boundary value problems to obtain strong a priori estimates. This is the meaning of these theorems.

a priori estimates of the solution , finite-dimensional Hilbert space , initial-boundary value problem , nonlinear equations , strong solution , weak solution

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Institute of Mathematics and Mathematical modeling, Almaty, Kazakhstan
International University of Information Technology, Almaty, Kazakhstan
M. Tynyshpaev Kazakh Academy of Transport and Communication, Almaty, Kazakhstan
H.A. Yasavi International Kazakh-Turkish University, Turkestan, Kazakhstan
Osh State University, Osh, Kyrgyzstan

Institute of Mathematics and Mathematical modeling
International University of Information Technology
M. Tynyshpaev Kazakh Academy of Transport and Communication
H.A. Yasavi International Kazakh-Turkish University
Osh State University

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