Spatial Heterogeneities in Nonlinear Parabolic Problems

Brief description:

The most realistic parabolic models in applied, or social, sciences and engineering are those with spatially heterogeneous coefficients, as in nature spatial (and temporal) heterogeneities determine not only the evolution of Earth ecosystems, but the evolution of the universe as a whole… since the Big-Bang. In this project we are proposing to analyze the effects of spatial heterogeneities on the dynamics of some paradigmatic models in Ecology and Environmental Sciences. The first one is a generalized class of logistic equations, where we expect to characterize their dynamics within the metasolutions regime by establishing the uniqueness of the underlying large solutions of the model. The second one is the diffusive Lotka-Volterra competition model, where we expect to characterize its dynamics for small diffusivities. The third one is a one-dimensional boundary value problem of degenerate type, with a vanishing weight function in front of the nonlinearity, where we expect to ascertain the internal fine structure of the set of nodal solutions in terms of a certain spectral parameter.


Julián López-Gómez (Full Proffessor, Faculty of Mathematics, UCM)
Sergio Fernández-Rincón (Contract FPU, University Personal under Formation, UCM)
Andrea Tellini (Juan de la Cierva Postdoctoral Contract, UCM)
Luis Maire Marín (Without contract, University Personal under Formation, UCM)