The Energy decay rate of 1D and 2D Timoshenko systems. Theoretical analysis and numerical simulation
Sabrine Chebbi (University of Tunisia, El MANAR, UTM)
Abstract: We focus on the behavior of the solutions of the Timoshenko systems in dimensions 1 and 2 using the lower bound estimates of the energy. We study a nonlinear damped one-dimensional thermo-elastic Timoshenko system where the heat flux is given by the Cattaneo’s law. After deriving the strong lower energy estimates, we show the optimality for some explicit examples. Furthermore, we discuss the well-posedness and the decay rate of the energy of the Mindlin-Timoshenko plate equations subject to a nonlinear dissipation acting on the rotation angles’equations. Later, we perform a numerical sim- ulation of the one-dimensional Timoshenko system, our approach is based on adequate use of the finite element and the finite difference methods giving rise to a new scheme which characterizes the asymptotic behavior of the discrete energy.
MathematicsPhysics
Audience: researchers in the topic
Nečas Seminar on Continuum Mechanics
Series comments: This seminar was founded on December 14, 1966.
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor).
Organizers: | Miloslav Feistauer, Petr Knobloch, Martin Kružík*, Šárka Nečasová* |
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