Dynamic von Karman equations with viscous damping

Author:

El-Aqqad B., ,Oudaani J.,El Mouatasim A., ,

Abstract

In this paper we are interested to the dynamic von Karman equations coupled with viscous damping and without rotational forces, (α=0) [Chueshov I., Lasiecka I. (2010)], this problem describes the buckling and flexible phenomenon of small nonlinear vibration of vertical displacement to the elastic plates. Our fundamental goal is to establish the existence and the uniqueness to the weak solution for the so-called global energy, under assumption F0∈H3+ϵ(ω). Finally for illustrate our theoretical results we use the finite difference method.

Publisher

Lviv Polytechnic National University

Subject

Computational Theory and Mathematics,Computational Mathematics

Reference8 articles.

1. Chueshov I., Lasiecka I. Von Karman Evolution, Well-posedness and Long Time Dynamics. New York, Springer (2010).

2. Ciarlet P. G., Rabier R. Les Equations de von Karman. Lecture Notes in Mathematics. Vol. 826. New York, Springer (1980).

3. Lions J. L., Magenes E. Problèmes aux Limites non Homogènes et Applications. Vol. 1. Gauthier-Villars, Paris, Dunod (1968).

4. Oudaani J., El Mouatasim A., El-Aqqad B. Uniqueness of Solution to the von Karman Equations with Free Boundary Conditions. Nonlinear Dynamics and Systems Theory. 20 (4), 425-438 (2020).

5. Oudaani J. Numerical approach to the uniqueness solution of von Karman evolution. International Journal of Mathematics in Operational Research. 13 (4), 450-470 (2018).

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