L.A. Medeiros

Vibrations of Elastic Strings: Mathematical Aspects, Part Two

AbstractDedicated to Professor Jacque-Louis Lions on the occasion of his 70th birthday We consider a mixed problem for the operator

Vibrations of elastic membranes with moving boundaries

\hat Lu\left( {x,t} \right) = \frac{{\partial ^2 u}}{{\partial t^2 }} - \left( {a\left( t \right) + b\left( t \right)\int_{\alpha \left( t \right)}^{\beta \left( t \right)} {\left( {\frac{{\partial u}}{{\partial x}}} \right)} ^2 dx} \right)\frac{{\partial ^2 u}}{{\partial x^2 }}

Finite approximate controllability for semilinear heat equations in noncylindrical domains

in a noncylindrical domain

On the existence of global solutions of a coupled nonlinear Klein-Gordon equations

\widehat Q

Vibrations of elastic string with nonhomogeneous material

. We obtain local solution in t. When we add a viscosity we obtain a global solution. We also investigate the asymptotic behavior of the energy.

On equations of Benjamin–Bona–Mahony type

This paper deals with the null controllability of an initial-boundary value problem for a parabolic coupled system with nonlinear terms of local and nonlocal kinds. The control is distributed in space and time and is exerted through one scalar function whose support can be arbitrarily small. We first prove that, if the initial data are sufficiently small and the linearized system at zero satisfies an appropriate coupling condition, the equations can be driven exactly to zero. We also present an iterative algorithm of the quasi-Newton kind for the computation of the control and we prove a convergence result. The behavior of this algorithm is illustrated with some numerical experiments.