Determination of coefficients for a dissipative wave equation via boundary measurements

AbstractIn this paper we consider the inverse problem of recovering the viscosity coefficient in a dissipative wave equation via boundary measurements. We obtain stability estimates by considering all possible measurements implemented on the boundary. We also prove that the viscosity coefficient is uniquely determined by a finite number of measurements on the boundary provided that it belongs to a given finite dimensional vector space

One-dimension cubic-quintic Gross-Pitaevskii equation in Bose-Einstein condensates in a trap potential

By means of new general variational method we report a direct solution for the quintic self-focusing nonlinearity and cubic-quintic 1D Gross Pitaeskii equation (GPE) in a harmonic confined potential. We explore the influence of the 3D transversal motion generating a quintic nonlinear term on the ideal 1D pure cigar-like shape model for the attractive and repulsive atom-atom interaction in Bose Einstein condensates (BEC). Also, we offer a closed analytical expression for the evaluation of the error produced when solely the cubic nonlinear GPE is considered for the description of 1D BEC.Comment: 6 pages, 3 figure

Superfluidity and collective oscillations of trapped Bose-Einstein condensates in a periodical potential

Based on a unified theoretical treatment of the 1D Bogoliubov-de Genes equations, the superfluidity phenomenon of the Bose-Einstein condensates (BEC) loaded into trapped optical lattice is studied. Within the perturbation regime, an all-analytical framework is presented enabling a straightforward phenomenological mapping of the collective excitation and oscillation character of a trapped BEC where the available experimental configurations also fit.Comment: 5 pages and 2 Figs, some errors have been corrected in versions

Propagación temporal de algunas enfermedades bacterianas: un modelo matemático

We introduce a new theoretical model to describe the dynamics of transmission for a certain class of bacterial infectious diseases. The propagation mechanism considered is the one concerning direct personal contact. Immunity factors, if present, will be ignored, but in our calculations is included the existence of an incubation period for the contagious infection. The effects of public health campaigns on the spread of the disease are also considered and the inclusion of a certain parameter å to measure the effciency of such attempts is proposed.Introducimos aqui un nuevo modelo teorico para describir la dinamica de transmision a que responden algunas enfermedades infecciosas bacterianas. El mecanismo de propagacion considerado es el de contacto personal directo. La presencia de factores de inmunidad es ignorada, pero el modelo incorpora la existencia de un periodo de incubacion para la enfermedad. Los posibles efectos de campanas educativas de salud publica, orientadas a controlar la propagacion, son incluidos y se introduce un cierto parametro �à para cuantificar la eficiencia de ese tipo de recurso

Spread in time of some bacterial infectious diseases: a mathematical model

Introducimos aquí un nuevo modelo teórico para describir la dinámica de transmisión a que responden algunas enfermedades infecciosas bacterianas. El mecanismo de propagación considerado es el de contacto personal directo. La presencia de factores de inmunidad es ignorada, pero el modelo incorpora la existencia de un período de incubación para la enfermedad. Los posibles efectos de campañas educativas de salud pública, orientadas a controlar la propagación, son incluidos y se introduce un cierto parámetro ¿ para cuantificar la eficiencia de ese tipo de recurso