Profesor Ayudante Doctor (Assistant Professor)
Department of Applied Mathematics and Mathematical Analysis
School of Mathematical Sciences
Complutense University of Madrid
Nonlinear Elliptic and Parabolic Equations UCM-GR17-970846

 

 

 

Bio

I obtained my PhD in Mathematics at Complutense University of Madrid under the supervision of Julián López-Gómez (UCM) and Fabio Zanolin (Udine University). During my PhD I have been supported by an UCM Predoctoral Fellowship. I have done three research stays during my PhD: Udine University (June 23-29, 2019; supervisor: Prof. F. Zanolin), Turin University (May 1 - August 1, 2021; supervisors: Profs. A. Boscaggin and W. Dambrosio), Turin University (November 14-20, 2021; supervisors: Profs. A. Boscaggin and W. Dambrosio). After completing my PhD Thesis in June 2023, I carried out a research stay (June 21 - July 21, 2023) as visiting professor at the University of Modena and Reggio Emilia with Profs. Elisa Sovrano and Valentina Taddei. I am currently part of the national research project PID2021-123343NB-I00: Heterogeneous Differential Equations: Dynamics and Numerics.

 

Research interests

Bifurcation and topological methods in general elliptic systems including spatial ecology and population systems, Poincaré-Birkhoff type theorems to the analysis of existence and multiplicity of subharmonic solutions in Hamiltonian systems, complex and chaotic dynamics through topological horseshoes theory, celestial mechanics via variational methods, wavefront solutions in degenerate reaction-diffusion systems.

 

Latest Publications

• 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, E. Muñoz-Hernández. A robust multiplicity result in a generalized diffusive predator-prey model. Advances in differential equations, volume 29, 5-6, pages 437-476. 2024. https://doi.org/10.57262/ade029-0506-437
• J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments. Open Mathematics. 2023, 21 (1), 1-54. Special Issue on Future Directions of Further Developments in Mathematics. https://doi.org/10.1515/math-2022-0593
• J. López-Gómez, E. Muñoz-Hernández. Large saturation effects provoke multiplicity in spatially heterogeneous predator-prey models. Proceedings of the XXVII Congreso de Ecuaciones Diferenciales y Aplicaciones / XVII Congreso de Matemática Aplicada, Prensas de la Universidad de Zaragoza, 2023. https://www.doi.org/10.26754/uz.978-84-18321-66-5
• J. López Gómez, E. Muñoz Hernández, F. Zanolin. Rich dynamics in planar systems with heterogeneous nonnegative weights. Communications on Pure and Applied Analysis. 2023. https://www.aimsciences.org/article/doi/10.3934/cpaa.2023020
• A. Boscaggin, W. Dambrosio, E. Muñoz-Hernández. A Maupertuis-type principle in relativistic mechanics and applications. Calculus of Variations and Partial Differential Equations, 2023, 62(95). https://doi.org/10.1007/s00526-023-02430-9
• A. Boscaggin, E. Muñoz-Hernández. Planar Hamiltonian systems: Index theory and applications to the existence of subharmonics. Nonlinear Analysis, 2023, vol. 226, 113142.  https://doi.org/10.1016/j.na.2022.113142

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