Two theorems on estimates for solutions of one class of nonlinear equations in a finite-dimensional space
Ақырлыөлшемдi кеңiстiктегi сызықты емес теңдеулердiң бiр класының шешiмiн бағалаудың екi теоремасы
Две теоремы об оценках решений одного класса нелинейных уравнений в конечномерном пространстве
Koshanov B.D. Kakharman N. Segizbayeva R.U. Sultangaziyeva Zh.B.
2022E.A. Buketov Karaganda University Publish house
Bulletin of the Karaganda University. Mathematics Series
2022#107Issue 370 - 84 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 and quantum physics. 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. In the first subsection, the notation used and the statement of the main results are given. In the second subsection, the main lemmas are given. The third section is devoted to the proof of Theorem 1. In the fourth section, Theorem 2 is proved. The conditions of the theorems are such that they can be used in studying a certain class of initial-boundary value problems to obtain strong a priori estimates in the presence of weak a priori estimates. This is the meaning of these theorems.
a priori estimate of solutions , differentiable vector-functions , finite-dimensional Hilbert space , invertible operator , nonlinear equations
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Al-Farabi Kazakh National University, Almaty, Kazakhstan
International University of Information Technology, Almaty, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Civil Aviation Academy, Almaty, Kazakhstan
Al-Farabi Kazakh National University
International University of Information Technology
Institute of Mathematics and Mathematical Modeling
Civil Aviation Academy
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