David Gómez-Castro

david.gomezcastro@uam.es

Departamento de Matemáticas, Universidad Autónoma de Madrid

Facultad de Ciencias, Módulo 17

Ciudad Universitaria de Cantoblanco

28049 Madrid, Spain

Upcoming events

July 2025: New Perspectives in Nonlocal and Nonlinear PDEs
Anacapri, Italy

Recently finished events

March 2025: julia course.
Universidad Complutense de Madrid, Spain
Feb. 2025: Seminar. NTNU, Norway.
Oct. 2024: Meeting of the Spanish “Nonlocal PDEs and Applications” Network. Universidad de Valencia, Spain.
July 2024: Summer School UIMP 2024: The Laplacian and Beyond. Celebrating the Mathematics of Luis Caffarelli
Santander, Spain
July 2024: EMS Conference.
Seville, Spain
June 2024: Homenaje a J.I. Díaz.
Madrid, Spain
April 2024: Aggregation-Diffusion Equations & Collective Behavior.
CIRM, Marseille, France

selected publications

Nonlinear Reaction-Diffusion Processes for Nanocomposites

J. I. Díaz , D. Gómez-Castro , and T. A Shaposhnikova

2021

DOI Bib

@book{diaz+gc+shaposhnikova2021book,
  address = {Berlin, Boston},
  author = {D{\'{i}}az, J. I. and Gómez-Castro, D. and Shaposhnikova, T. A},
  doi = {10.1515/9783110648997},
  isbn = {978-3-11-064899-7},
  publisher = {De Gruyter},
  title = {{Nonlinear Reaction-Diffusion Processes for Nanocomposites}},
  url = {https://www.degruyter.com/view/title/551325},
  year = {2021},
  keywords = {short-cv, selected},
  dimensions = true
}

J39

Partial Mass Concentration for Fast-Diffusions with Non-Local Aggregation Terms

José A. Carrillo , David Gómez-Castro , and Alejandro Fernández-Jiménez

Journal of Differential Equations, 2024

DOI arXiv Bib

@article{Carrillo+Fernandez-Jimenez+GC2024JDE,
  title = {Partial Mass Concentration for Fast-Diffusions with Non-Local Aggregation Terms},
  author = {Carrillo, José A. and Gómez-Castro, David and Fernández-Jiménez, Alejandro},
  date = {2024},
  journal = {Journal of Differential Equations},
  volume = {409},
  pages = {700-773},
  year = {2024},
  issn = {0022-0396},
  doi = {10.1016/j.jde.2024.08.013},
  arxivid = {2304.04582},
  primaryclass = {math.AP},
  keywords = {short-cv,selected},
  dimensions = true
}

J36

Beginner’s guide to Aggregation-Diffusion Equations

David Gómez-Castro

SeMA Journal, 2024

DOI arXiv Bib

@article{GCbegginers2024,
  title = {Beginner's guide to Aggregation-Diffusion Equations},
  author = {Gómez-Castro, David},
  journal = {SeMA Journal},
  year = {2024},
  doi = {10.1007/s40324-024-00350-y},
  arxivid = {2309.13713},
  eprint = {2309.13713},
  eprinttype = {arxiv},
  primaryclass = {math.AP},
  keywords = {short-cv,selected},
  dimensions = true
}

J34

Asymptotic simplification of Aggregation-Diffusion equations towards the heat kernel

José A. Carrillo , D. Gómez-Castro , Yao Yao , and Chongchun Zeng

Archive for Rational Mechanics and Analysis, 2023

Abs DOI arXiv

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at infinity, then the linear diffusion overcomes its effect, either attractive or repulsive, for large times independently of the initial data, and solutions behave like the fundamental solution of the heat equation with some rate. The potential W(x) ∼\log |x| for |x| ≫1 appears as the natural limiting case when the intermediate asymptotics change. In order to obtain such a result, we produce uniform-in-time estimates in a suitable rescaled change of variables for the entropy, the second moment, Sobolev norms and the C^αregularity with a novel approach for this family of equations using modulus of continuity techniques.
J27
Characterisation of homogeneous fractional Sobolev spaces

Lorenzo Brasco , D. Gómez-Castro , and J. L. Vázquez

Calculus of Variations and Partial Differential Equations, 2021

Abs DOI arXiv Bib

Our aim is to characterize the homogeneous fractional Sobolev–Slobodeckiĭ spaces $\mathcal D^s,p (\mathbb R^n) D s , p ( R n ) and their embeddings, for s ∈(0,1] s ∈ ( 0 , 1 ] and p\ge 1 p ≥ 1 . They are defined as the completion of the set of smooth and compactly supported test functions with respect to the Gagliardo–Slobodeckiĭ seminorms. For s p < n s p < n or s = p = n = 1 s = p = n = 1 we show that \mathcal D^s,p(\mathbb R^n) D s , p ( R n ) is isomorphic to a suitable function space, whereas for s p \ge n$ s p ≥ n it is isomorphic to a space of equivalence classes of functions, differing by an additive constant. As one of our main tools, we present a Morrey–Campanato inequality where the Gagliardo–Slobodeckiĭ seminorm controls from above a suitable Campanato seminorm.
@article{Brasco+GC+Vazquez2021, archiveprefix = {arXiv}, arxivid = {2007.08000}, author = {Brasco, Lorenzo and Gómez-Castro, D. and V{\'{a}}zquez, J. L.}, doi = {10.1007/s00526-021-01934-6}, issn = {0944-2669}, journal = {Calculus of Variations and Partial Differential Equations}, number = {2}, title = {{Characterisation of homogeneous fractional Sobolev spaces}}, url = {http://link.springer.com/10.1007/s00526-021-01934-6}, volume = {60}, year = {2021}, keywords = {short-cv,selected}, dimensions = true }