In this work, the ecologically well-posedness of a predator-prey model is demonstrated by showing that a region of the first quadrant is a positively invariant attracting set for the solutions of that model. The predator-prey model considers logistic-type growth in both populations and a non-differentiable functional response that generalizes previous ones. Due to non-differentiability, there is no uniqueness of solutions, and the standard methodology cannot be applied directly. Topological equivalences, geometrical arguments, and the Poincare-Bendixson theorem are used to obtain our result.

The duality theory of convex analysis is applied to the complete electrode model (CEM), which is a standard model in electrical impedance tomography (EIT). This results in a dual formulation of the CEM and a general error estimate. This new formulation of the CEM is written in terms of current fields and is shown to have a unique solution. Using this formulation, the general error estimate is proved, from which two a posteriori error estimates and a well known asymptotic result on CEM solutions are obtained. The first a posteriori error estimate assesses the accuracy of solutions to approximate problems, and the second one assesses the accuracy of approximate solutions. Numerical tests to apply this second estimate are performed, employing the finite element method to obtain approximate solutions.

Estudia el efecto de un contaminante en una interacción depredador-presa, considerando específicamente un entorno acuático. Esta tesis tiene dos partes, en la primera, estudia un sistema de ecuaciones diferenciales ordinarias que modela la dinámica de la interacción depredador-presa en un medio acuático contaminado, tomando como base el modelo depredador-presa Lotka-Volterra. Muestra que la coexistencia de las poblaciones es condicionada por las densidades poblacionales y la concentración del contaminante en el medio. En la última parte, propone un modelo más realista para la interacción depredador-presa en un medio acuático contaminado. La respuesta funcional tiene forma general y existe competencia intraespecífica en las presas. Bajo ciertas restricciones sobre el contaminante, estudia los modelos Volterra y Rosenzweig-MacArthur afectados por un contaminante. En ambas parte...