Seminar Mechanics of Machines and Mechanisms - Models and Mathematical Methods

 

PROGRAM

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Plan rada Seminara Mehanika mašina i mehanizama - modeli i matematičke metode za OKTOBAR 2024.

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Utorak, 29.10.2024. u 17:00, sala 301f, Kneza Mihaila 36 i Live stream
Isidora Rapajić, Mathematical Institute SANU, Belgrade
STABILITY ANALYSIS IN WASHBURN'S MODEL OF CAPILLARY FLOW
Washburn's equation is a widely used model of capillary flow. This nonlinear, second-order ODE can be derived from the first principles, specifically the mass balance and the integral form of the momentum balance. In this lecture, we will present the derivation of Washburn's equation with a slip condition on the pipe wall. The stationary state will be determined, and linear stability will be examined. Starting with an eigenvalue analysis, we will show that the equilibrium height may be reached either monotonically or oscillatory, depending on the value of a critical parameter. Using energy estimate, we will demonstrate that the solution to Washburn's equation is bounded. Moreover, by applying Lyapunov's theorem and the LaSalle principle (Krasovski's theorem), we will prove that for a certain family of initial conditions, all solutions converge to the stationary solution.
Joint work with Prof. Srboljub Simić.

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Seminar Mehanika mašina i mehanizama - modeli i matematičke metode započeo je sa radom u junu 2018.god. Seminar se održava do dva puta mesečno, utorkom u periodu od 17.00 - 19.00 u Matematičkom institutu SANU.

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