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We consider a linear dissipative wave equation in IRN with periodic coefficients. By means of Bloch wave decomposition, we obtain an expansion of solutions as t ! 1 and conclude that, in a first approximation, the solutions behave as the homogen[...]texto impreso
We consider the finite-difference and finite-element space discretization of the 1 - d wave equation with homogeneous Dirichlet boundary conditions in a bounded interval. We analyze the problem of estimating the total energy of solutions in term[...]texto impreso
We consider space semi-discretizations of the 1 ? d wave equation in a bounded interval with homogeneous Dirichlet boundary conditions. We analyze the problem of boundary observability,i.e., the problem of whether the total energy of solutions c[...]texto impreso
The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic[...]texto impreso
In this note we consider a star-shaped network of vibrating strings. The problem of controllability when one control acts on the junction point is considered. A simple proof is given that, in particular, does not use Ingham inequalities, of the [...]texto impreso
Las Matemáticas constituyen uno de los más importantes bienes culturales de nuestra civilización. Su presencia es palpable en prácticamente todos los ámbitos de la actividad humana: desde la científica hasta la vida cotidiana. Probablemente en e[...]texto impreso
We consider the 1 - d wave equation epsilon u(tt) - u(tt) + u(t) = 0 With Dirichlet boundary conditions in a bounded interval. It is well known that for any epsilon > 0 this system is exactly controllable, with controls distributed on some open[...]texto impreso
In this paper we prove that the null controllability property of the heat equation may be obtained as limit of the exact controllability properties of singularly perturbed damped wave equations, We impose Dirichlet, homogeneous boundary conditio[...]texto impreso
Doubova, Anna ; Fernández Cara, E. ; González Burgos, Manuel ; Zuazua Iriondo, Enrique | Siam Publications | 2002We present some results concerning the controllability of a quasi-linear parabolic equation (with linear principal part) in a bounded domain of ${\mathbb R}^N$ with Dirichlet boundary conditions. We analyze the controllability problem with distr[...]texto impreso
This paper is devoted to study the property of bservability for wave equations guaranteeing that the total energy of solutions may be estimated by means of the energy concentrated on a subset of the domain or of the boundary. We prove that this [...]texto impreso
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Rodríguez del Río, Roberto ; Zuazua Iriondo, Enrique | Universidad de La Frontera, Temuco, Chile | 2003-06En este trabajo se describe la génesis de las series de Fourier a través de los trabajos pioneros de finales del siglo XVIII y principios del XIX en la resolución de dos de las Ecuaciones en Derivadas Parciales (EDP) más importantes: la ecuación[...]texto impreso
We address three null controllability problems related to the $1-d$ heat equation. First we show that the $1-d$ heat equation with a rapidly oscillating density is uniformly null controllable as the period of the density tends to zero. We also p[...]texto impreso
Mathematics is one of the most important cultural goods of our civilization. Its presence is tangible in all the fields of human activity: from scientific activity to daily life. We are probably agreed on that. Once the importance of Mathematics[...]texto impreso
We consider the 1-d heat equation with a rapidly oscillating periodic, C-2 density in a bounded interval with Dirichlet boundary conditions. We analyze the problem of the null-controllability with a control acting on one of the extremes of the i[...]
