Institutos Universitarios

Spatial and temporal heterogeneities in Nonlinear parabolic problems

Brief description

The most realistic parabolic models in Population Dynamics, Reaction-Diffusion equations and Fluid Dynamics are those incorporating spatial and temporal heterogeneities in its formulation, as in Nature most of phenomenology’s are seasonal and spatial heterogeneities are the general rule, for as the amount of solar energy received depends on the precise location. In this project we are going to analyze the effects of the spatial and temporal heterogeneities on the dynamics of some paradigmatic models in Ecology, Reaction-Diffusion and Fluid Dynamics, including periodic-parabolic predator prey and competition systems. Among the expected results are the following: (a) establishing that seasonal effects in predator-prey systems provoke chaos; (b) finding out what are the aspects of the spatial heterogeneities provoking complexity; (c) finding out the optimal conditions for the existence of a priori bounds in superlinear indefinite BVP’s.



  • Julián López Gómez. Professor (Catedrático), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM (PI)
  • Juan Carlos Sampedro Pascal. Associate Professor (Profesor Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM
  • Eduardo Muñoz Hernández. Associate Professor (Profesor Titular), School of Mathematical Sciences (Facultad de CC Matemáticas), UCM


External Collaborators

  • Paul H. Rabinowitz. Emeritus Professor, Department of Mathematics, Centre University of Wisconsin-Madison
  • Fabio Zanolin. Emeritus Professor, Department of Mathematics, Centre Università degli Studi di Udine
  • Pierpaolo Omari. Emeritus Professor, Department of Mathematics, Centre Università degli Studi di Trieste
  • Santiago Cano Casanova. Director, Department of Mathematics (Departamento de Matemáticas), Centre Pontifica Comillas University of Madrid
  • Andrea Tellini. Associate Professor (Profesora Contratada Doctora), Department of Applied Mathematics to Industrial Engineering (Departamento de Matemática Aplicada a la Ingeniería Industrial), UPM
  • Luis Maire Martín. Associate Professor (Profesor Contratado Doctor), Department of Applied Mathematics and Informatics to Civil and Naval Engineering (Departamento de Matemática e Informática Aplicadas a la Ingeniería Civil y Naval), UPM
  • Sergio Fernández Rincón. Assistant Professor, Department of Mathematics, Francisco de Vitoria University,
  • Inmaculada Antón López. Associate Professor (Profesora Titular), Departament of Mathematical Analysis and Applied Mathematics (Departamento de Análisis Matemático y Matemática Aplicada), UCM.
  • Pablo Cubillos Rodríguez. PhD Student of the IMEIO program, UCM.