This work concerns with the existence of the time optimal controls for some linear evolution equations without the a priori assumption on the existence of admissible controls. Both global and local existence results are presented. Some necessary conditions, sufficient conditions, and necessary and sufficient conditions for the existence of time optimal… (More)
Strictly convex functions and coercive fields in the Riemann metric for hyperbolic and non-hyperbolic
We consider a dynamic linear shallow shell model, subject to nonlinear dissipation active on a portion of its boundary in physical boundary conditions. Our main result is a uniform stabilization theorem which states a uniform decay rate of the resulting solutions. Mathematically, the motion of a shell is described by a system of two coupled partial… (More)
It is shown that on certain Banach spaces, including C[0, 1] and L 1 [0, 1], there is no strongly continuous semigroup (T t) 0<t <1 consisting of weakly compact operators such that (T t) 0<t <1 is an R-bounded family. More general results concerning approximating sequences are included and some variants of R-boundedness are also discussed.
We study a controllability problem (exact in the mechanical variables ww w t and, simultaneously, approximate in the thermal variable θ) of thermo-elastic plates by means of boundary controls, in the hinged/Dirichlet BC case, when the " thermal expansion " term is variable in space. 2 be an open bounded domain with smooth boundary. We shall here consider… (More)
An extended theory for elastic and plastic beam problems is studied. By introducing new dependent and independent variables, the standard Timoshenko beam model is extended to take account of shear variation in the lateral direction. The dynamic governing equations are established via Hamilton's principle, and existence and uniqueness results for the… (More)