Gulkanov Aleksandr
Публикации:
Гасанов М. В., Гулканов А.,
Analytical Solution of the Rayleigh – Plesset Equation Filled with Van Der Waals Gas for Various Isoprocesses
2024, vol. 20, no. 1, с. 3-13
Подробнее
In this paper, we consider a mathematical model of the dynamics of the behavior of a spherically
symmetric Rayleigh – Plesset bubble in the van der Waals gas model. The analysis of the
model takes into account various isoprocesses without the presence of condensation and a model
that takes into account condensation in an isothermal process. In each case, various characteristics
are searched for, such as oscillation frequency (linear/small oscillations), damping factor,
relaxation time, decrement, and logarithmic decrement. Solutions are found in quadratures for
various parameters of the equation. The theoretical results obtained are compared with the
results of the numerical solution of the Cauchy problem for various isoprocesses.
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Гасанов М. В., Гулканов А.
A Study of a Mathematical Model with a Movable Singular Point in a Fourth-Order Nonlinear Differential Equation
2023, vol. 19, no. 4, с. 575-584
Подробнее
This article introduces a mathematical model that utilizes a nonlinear differential equation to study a range of phenomena such as nonlinear wave processes, and beam deflections. Solving this equation is challenging due to the presence of moving singular points. The article addresses two main problems: first, it establishes the existence and uniqueness of the solution of the equation and, second, it provides precise criteria for determining the existence of a moving singular point. Additionally, the article presents estimates of the error in the analytical approximate solution and validates the results through a numerical experiment. |