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.

 

Researchers

• 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.

 

Publications

• J. López-Gómez and J. C. Sampedro. Blow-up estimates and a priori bounds for the positive solutions of a class of superlinear indefinite elliptic problems. Nonlinear Analysis, 251. 2025. DOI: 10.1016/j.na.2024.113693.
• S. Cano-Casanova, S. Fernández-Rincón, J. López-Gómez. A singular perturbation result for a class of periodic-parabolic BVPs. Open Mathematics, 22 (1). 2024. DOI: 10.1515/math-2024-0020.
• J. López-Gómez, P. H. Rabinowitz, F. Zanolin. Non-negative solutions of a sublinear elliptic problem. Journal of Fixed Point Theory and Applications, 26. 2024. DOI: 10.1007/s11784-024-01120-z.
• P. Cubillos, J. López-Gómez, A. Tellini. High multiplicity of positive solutions in a superlinear problem of Moore–Nehari type. Communications in Nonlinear Science and Numerical Simulation, 136. 2024. DOI: 10.1016/j.cnsns.2024.108118.
• J. López-Gómez, V.K. Ramos, C.A. Santos, A. Suárez. Point-wise behavior of the explosive positive solutions to a degenerate elliptic BVP with an indefinite weight function. Journal of Differential Equations, 403, 67–86. 2024. DOI: 10.1016/j.jde.2024.05.006.
• J. López-Gómez, E. Muñoz-Hernández. Minimal complexity and chaos in periodic predator-prey models. Rendiconti del Seminario Matematico di Torino, 81 (1), 133 – 158. 2023. Link: http://www.seminariomatematico.polito.it/rendiconti/81-1.html.
• J. López-Gómez, J. C. Sampedro. Bifurcation Theory for Fredholm Operators. Journal of Differential Equations, 404, 182-250, 2024. DOI: 10.1016/j.jde.2024.05.040.
• J. C. Sampedro. On the Lp-Spaces of Projective Limits of Probability Measures. Journal of Theoretical Probability. DOI: 10.1007/s10959-024-01329-1.
• J. C. Sampedro. On the colimits of certain Sobolev spaces. Journal of Mathematical Analysis and Applications, 535 (2). 2024. DOI: 10.1016/j.jmaa.2024.128141.

News

• 27 November 2023. Four IMI members and four members of its Scientific Committee are in the lists of the most highly cited scientists worldwide, published by Stanford University.  The selection is based on the top 100,000 scientists by c-score or a percentile rank of 2% or above in the sub-field. The four IMI members mentioned are Juan Luis Vázquez Suárez, Julián López-Gómez, Jesús Ildefonso Díaz Díaz and Francisco Javier Montero de Juan. Also appearing in the same lists are IMI Scientific Committee members Paul Rabinowitz, Simon Donaldson, Herbert Amann and Dikran Dikranjan.