Institutos Universitarios

  1. Portada
  2. Programmes
  3. 2020-present
  4. Spatial and Temporal Heterogeneities in Nonlinear Parabolic Problems

Spatial and Temporal Heterogeneities in Nonlinear Parabolic Problems

Brief description

The most realistic parabolic models in the applied sciences are those with spatially and temporally heterogeneous coefficients, for as in Nature these heterogeneities determine not only the evolution of Ecosystems, but the evolution of the Universe as a whole. The aim of this Project is analyzing the effects of the spatial and temporal heterogeneities on the dynamics of some paradigmatic models in Ecology, Environmental Sciences and Physics. To analyze the effects of temporal heterogeneities we will use a classical periodic predator-prey model with to ascertain the global structure of its set of subharmonics. To analyze the effects of the spatial heterogeneities we will use: (a) the diffusive Lotka-Volterra competition model, where we expect to characterize the dynamics for sufficiently small diffusion coefficients, (b) a quasilinear problem related to the mean curvature operator, were we expect to characterize the interplay between the regular and the singular solutions, and (c) a one-dimensional bvp of degenerate type, with a vanishing weight in front of the nonlinearity, where we expect to ascertain the global structure of the set of nodal solutions.

 

Researchers

 

External Collaborators

  • Inmaculada Antón López. (Profesional, Facultad de Matemáticas, UCM)
  • Paul Rabinowitz. University of Wisconsin-Madison
  • Fabio Zanolin. University of Udine
  • Pierpaolo Omari. University of Trieste
  • Andrea Tellini. Polytechnic University of Madrid 
  • David González de la Aleja Gallego. King Juan Carlos University 

 

Publications

  • 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, J. C. Sampedro, Orientability through the algebraic multiplicity. Journal of Fixed Point Theory Applications. 2023, 25, Art. Number: 60. https://doi.org/10.1007/s11784-023-01062-y
  • 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
  • G. Feltrin, J. C. Sampedro, F. Zanolin. Periodic solutions to superlinear indefinite planar systems: A topological degree approach. Journal of Differential Equations, 2023, 363, 5. https://doi.org/10.1016/j.jde.2023.03.042
  • J. López Gómez, E. Muñoz Hernández, F. Zanolin. Rich dynamics in planar systems with heterogeneous nonnegative weights. Communications on Pure and Applied Analysis. 2023. volumen 22, 1043-1098.https://www.aimsciences.org/article/doi/10.3934/cpaa.2023020
  • J. L. Gómez, J. C. Sampedro. Generating loops and isolas in semilinear elliptic BVP's. Nonlinear Analysis, volumen 232, 2023, 113268, ISSN 0362-546X. https://doi.org/10.1016/j.na.2023.113268
  • 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
  • J. López-Gómez, P. Omari. Optimal regularity results for the one-dimensional prescribed curvature equation via the strong maximum principle. Journal of Mathematical Analysis and Applications, 2023, 512(2). https://doi.org/10.1016/j.jmaa.2022.126719
  • 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
  • J. C. Sampedro. Approximation Schemes for Path Integration on Riemannian Manifolds. Journal of Mathematical Analysis and Applications. 2022, 512, 2, Article number 126176. https://doi.org/10.1016/j.jmaa.2022.126176
  • M. Fencl, J. López-Gómez. Global bifurcation diagrams of positive solutions for a class of 1D superlinear indefinite problems. Nonlinearity. 2022, 35, 3, 1213 - 1248. https://doi.org/10.1088/1361-6544/ac4a88
  • P. Cubillos, J. Lopez-Gomez, A. Tellini. Multiplicity of nodal solutions in classical non-degenerate logistic equations. Electronic Research Archive. 2022, 30, 3, 898-928. https://doi.org/10.3934/era.2022047
  • J. López-Gómez, P. Omari. Branches of positive solutions of a superlinear indefinite problem driven by the one-dimensional curvature operator. Applied Mathematics Letters. 2022, 126, 107807. https://doi.org/10.1016/j.aml.2021.107807
  • J. López-Gómez, J. C. Sampedro. Axiomatization of the degree of Fitzpatrick, Pejsachowicz and Rabier. Journal of Fixed Point Theory and Applications. 2022, 24, 1, Article number 8. https://doi.org/10.1007/s11784-021-00916-7
  • W. T. Li, J. López-Gómez, J. W. Sun. Sharp Blow-Up Profiles of Positive Solutions for a Class of Semilinear Elliptic Problems. Advanced Nonlinear Studies. 2021, 21, 4, 751-765. https://doi.org/10.1515/ans-2021-2149
  • J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. Minimal complexity of subharmonics in a class of planar periodic predator-prey models. Proceedings of the XXVI Congreso de Ecuaciones Diferenciales y Aplicaciones. XVI Congreso de Matematica Aplicada. 2021, 258-264. Link.
  • W. T. Li, J. López-Gómez, J. W. Sun. Sharp Blow-Up Profiles of Positive Solutions for a Class of Semilinear Elliptic Problems. Advanced Nonlinear Studies. 2021. https://doi.org/10.1515/ans-2021-2149
  • J. López Gómez, E. Muñoz Hernández, F. Zanolin. Minimal complexity of subharmonics in a class of planar periodic predator-prey models. Proceedings of the XXVI Congreso de Ecuaciones Diferenciales y Aplicaciones. XVI Congreso de Matemática Aplicada. 2021, 258–264. ISBN: 978-84-18482-21-2 https://digibuo.uniovi.es/dspace/handle/10651/59093
  • E. Muñoz Hernández. Subharmonics in a class of planar periodic predator-prey models. Proceedings of the 3rd BYMAT Conference. 2021, 2, 31–34.ISSN: 2660-6003 https://temat.es/monograficos/article/view/vol2-p31
  • J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. The Poincaré-Birkhoff Theorem for a Class of Degenerate Planar Hamiltonian Systems. Advanced Nonlinear Studies. 2021, 21, 3, 489 – 499. https://doi.org/10.1515/ans-2021-2137
  • J. López-Gómez, J. C. Sampedro. New analytical and geometrical aspects of the algebraic multiplicity. Journal of Mathematical Analysis and Applications. 2021, 504, 1, 125375. https://doi.org/10.1016/j.jmaa.2021.125375
  • J. López-Gómez, J. C. Sampedro. Global Perturbation of Nonlinear Eigenvalues. Advanced Nonlinear Studies. 2021, https://doi.org/10.1515/ans-2021-2127
  • W. T. Li, J. López-Gómez, J. W. Sun. Sharp patterns of positive solutions for some weighted semilinear elliptic problems. Calculus of Variations and Partial Differential Equations. 2021, 60, Article number 85. https://doi.org/10.1007/s00526-021-01993-9
  • J. López-Gómez, E. Muñoz-Hernández. A spatially heterogeneous predator-prey model. Discrete and Continuous Dynamical Systems Series B. 2021, 26(4), 2085-2113. https://www.aimsciences.org/article/doi/10.3934/dcdsb.2020081 
  • S. Fernández-Rincón, J. López-Gómez. The Picone identity: A device to get optimal uniqueness results and global dynamics in Population Dynamics. Nonlinear Analysis: Real World Applications. 2021, 60, Article number 103285. https://doi.org/10.1016/j.nonrwa.2020.103285
  • J. López-Gómez, J. C. Sampedro. Algebraic multiplicity and topological degree for Fredholm operators. Nonlinear Analysis. 2020, 201, 112019. https://doi.org/10.1016/j.na.2020.112019
  • J. López-Gómez, P. Omari. Regular Versus Singular Solutions in a Quasilinear Indefinite Problem with an Asymptotically Linear Potential. Adv. Nonlinear Stud. 2020, 20(3), 557–578. https://doi.org/10.1515/ans-2020-2083
  • J. López-Gómez, L. Maire, L. Véron. General uniqueness results for large solutions. Zeitschrift fur Angewandte Mathematik und Physik. 2020, 71 (4), art. no. 109. DOI: https://doi.org/10.1007/s00033-020-01325-5
  • D. Aleja, I. Antón, J. López-Gómez, Global structure of the periodic positive solutions for a general class of periodic-parabolic logistic equations with indefinite weights. Journal of Mathematical Analysis and Applications, 2020; 487, 1, 123961. https://doi.org/10.1016/j.jmaa.2020.123961
  • D. Aleja, I. Antón, J. López-Gómez. Solution components in a degenerate weighted BVP. Nonlinear Analysis, Theory, Methods and Applications. 2020, 192, 111690. https://doi.org/10.1016/j.na.2019.111690 
  • J. López-Gómez. Protection Zones in Periodic-Parabolic Problems. Advanced Nonlinear Studies. 2020, 20, 2. https://doi.org/10.1515/ans-2020-2084
  • J. López-Gómez, E. Muñoz-Hernández. Global structure of subharmonics in a class of periodic predator-prey models. Nonlinearity. 2020, 33, 1. DOI: https://doi.org/10.1088/1361-6544/ab49e1
  • J. López-Gómez, E. Muñoz-Hernández, F. Zanolin. On the applicability of the Poincaré–Birkhoff twist theorem to a class of planar periodic predator-prey models. Discrete and Continuous Dynamical Systems Series A. 40(4): 2020, 2393-2419. https://www.aimsciences.org/article/doi/10.3934/dcds.2020119 
  • J. López-Gómez, P. Omari. Characterizing the formation of singularities in a superlinear indefinite problem related to the mean curvature operator. Journal of Differential Equations. 2020, 269, 2, 1544-1570. https://www.sciencedirect.com/science/article/pii/S0022039620300218
  • J. López-Gómez, P. H. Rabinowitz. The structure of the set of 1-node solutions of a class of degenerate BVP’s. J. Differential Equations. 2020, 268, 8, 4691-4732. https://doi.org/10.1016/j.jde.2019.10.040

News

  • 1 de diciembre de 2022. Tres miembros del IMI y tres miembros de su Comité Científico en los listados publicados por la Universidad de Stanford para dar a conocer los científicos con mayor número de citas a nivel mundial. Los listados incluyen a los 100.000 científicos con mayor c-score según métricas de SCOPUS (con y sin autocitas) o los que se encuentren entre el 2% de los más citados de su campo de investigación. El primer miembro del IMI en aparecer en los listados de citas a lo largo de una carrera, con datos de 1960 a 2021, es Juan Luis Vázquez Suárez, seguido de Julián López Gómez y Jesús Ildefonso Díaz Díaz. También aparecen en los mismos listados los miembros del Comité Científico Paul Rabinowitz, Simon Donaldson y Herbert Amann.