scholarly journals Long-time dynamics of vectorial von Karman system with nonlinear thermal effects and free boundary conditions

2018 ◽  
Vol 23 (3) ◽  
pp. 1037-1072 ◽  
Author(s):  
Irena Lasiecka ◽  
◽  
To Fu Ma ◽  
Rodrigo Nunes Monteiro ◽  
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Thermal Effects ◽  
Time Dynamics ◽  
Free Boundary Conditions ◽  
Von Karman ◽  
Long Time ◽  
Von Kármán System ◽  
Von Kármán ◽  
Long Time Dynamics

Timoshenko's beam equation as limit of a nonlinear one-dimensional von Kármán system

2000 ◽  
Vol 130 (4) ◽  
pp. 855-875 ◽  
Author(s):  
G. Perla Menzala ◽  
E. Zuazua
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Weak Limit ◽  
Beam Equation ◽  
Limit System ◽  
One Dimensional ◽  
Various Boundary Conditions ◽  
Von Karman ◽  
Von Kármán System ◽  
Von Kármán

We consider a dynamical one-dimensional nonlinear von Kármán model depending on one parameter ε > 0 and study its weak limit as ε → 0. We analyse various boundary conditions and prove that the nature of the limit system is very sensitive to them. We prove that, depending on the type of boundary condition we consider, the nonlinearity of Timoshenko's model may vanish.

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