Research Group on Nonlinear Partial Differential Equations

Description

The main objective of this research group is to develop new methods for nonlinear partial differential equations that allow us to contribute to the solution of concrete problems, most of them suggested by applications. Nonlinear phenomena in partial differential equations are a central theme in their application to science, engineering and industry, and in the modern theoretical development of the theory of partial differential equations itself.

In this group we will focus on the study of some nonlinear partial differential equations that model problems coming from different areas such as: image processing, materials science and crystal growth, phase transition problems whose free energy functional has linear growth with respect to the gradient, nonlinear diffusion problems and hydrodynamic radiation theory. In telegraphic form the topics we are interested in are the following:

Degenerate parabolic equations with saturated flow.
Models for the dynamics of granular materials.
Degenerate hyperbolic-parabolic equations.
Diffusion equations with gradient-dependent terms.
Non-linear elliptic equations involving measured data.
The inhomogeneous Dirichlet problem for the p-Laplacian.
Uniqueness for elliptic equations with lower-order terms.
Non-local evolution problems.
The 1-harmonic flow.

Goals CT

Regularity of the solutions of the relativistic heat equation.
Reaction-diffusion problems (Fisher-Kolmogorov, Patlak-Keller-Segel, etc.) with diffusion relative to the relativistic equation.
Existence of solutions for diffusion equations with gradient-dependent terms.
Mass transport problems.
Existence and uniqueness for 1-harmonic flow.

Research lines

Partial differential equations

To develop new methods for non-linear partial differential equations that allow us to contribute to the solution of concrete problems, most of them suggested by applications.

Management

MAZON RUIZ, JOSE M
PDI-Emerit/a Universitat

View details

Members

SEGURA DE LEON, SERGIO
PDI-Catedratic/a d'Universitat
Coordinador/a de Programa de Doctorat

View details

TOLEDO MELERO, JOSE JULIAN
PDI-Catedratic/a d'Universitat

View details

Scientific production by UV researcher

SEGURA DE LEON, SERGIO
PDI-Catedratic/a d'UniversitatCoordinador/a de Programa de Doctorat
ContraerExpandir
- B. Abdellaoui, A. Dall'Aglio; S. Segura de León(2017)Research Group on Nonlinear Partial Differential EquationsAdvanced Nonlinear Studies, 17(2), pp. 333 - 354. ISSN: 1536-1365
- M. Latorre; S. Segura de León(2017)Research Group on Nonlinear Partial Differential EquationsRendiconti Lincei-Matematica e Applicazioni, 28(4), pp. 817 - 859. ISSN: 1120-6330
- A. Molino Salas; S. Segura de León(2018)Research Group on Nonlinear Partial Differential EquationsNonlinear Analysis-Theory Methods & Applications, 168, pp. 50 - 66. ISSN: 0362-546X
- M. Latorre; S. Segura de León(2018)Research Group on Nonlinear Partial Differential EquationsJournal Of Evolution Equations, 18(1), pp. 1 - 28. ISSN: 1424-3199
- M. Latorre; S. Segura de León(2018)Research Group on Nonlinear Partial Differential EquationsJournal of Mathematical Analysis and Applications, 464(2), pp. 1051 - 1081. ISSN: 0022-247X
- V. De Cicco; D. Giachetti; S. Segura de León(2019)Research Group on Nonlinear Partial Differential EquationsJournal of the London Mathematical Society, 99(2), pp. 349 - 376. ISSN: 0024-6107
- A. Dall'Aglio; S. Segura de León(2019)Research Group on Nonlinear Partial Differential EquationsCzechoslovak Mathematical Journal, 69(2), pp. 379 - 390. ISSN: 0011-4642
- A. Dall'Aglio; S. Segura de León(2019)Research Group on Nonlinear Partial Differential EquationsRicerche di Matematica, 68(2), pp. 597 - 614. ISSN: 0035-5038
- B. de la Calle Ysern; J. C. Sabina de Lis; S. Segura de León(2020)Research Group on Nonlinear Partial Differential EquationsJournal of Mathematical Analysis and Applications, 484(1). ISSN: 0022-247X
- T. Leonori; A. Molino Salas; S. Segura de León(2021)Research Group on Nonlinear Partial Differential EquationsCommunications in Contemporary Mathematics, 23(1). ISSN: 0219-1997
- M. Latorre; M. Magliocca; S. Segura de León(2021)Research Group on Nonlinear Partial Differential EquationsRevista Matematica Complutense, 34(2), pp. 297 - 356. ISSN: 1139-1138
- M. Latorre; F. Oliva; F. Petitta; S. Segura de León(2021)Research Group on Nonlinear Partial Differential EquationsNonlinearity, 34(3), pp. 1791 - 1816. ISSN: 0951-7715
- A. Ferone; A. Mercaldo; S. Segura de León(2021)Research Group on Nonlinear Partial Differential EquationsESAIM: Control Optimisation and Calculus of Variations, 27. ISSN: 1262-3377
- J. C. Sabina de Lis; S. Segura de León(2021)On the limit, as p->1, of the higher eigenvalues problems for the p-Laplacian operator.Indiana University Mathematics Journal, 70(4), pp. 1395 - 1439. ISSN: 0022-2518
- J.C. Ortiz; M.T.O. Pimenta; S. Segura de León(2021)Research Group on Nonlinear Partial Differential EquationsNodea-Nonlinear Differential Equations and Applications, 28(6). ISSN: 1021-9722
- A. Molino Salas; S. Segura de León(2022)Research Group on Nonlinear Partial Differential EquationsPublicacions Matematiques, 66(1), pp. 269 - 304. ISSN: 0214-1493
- M. Latorre; S. Segura de León(2022)Research Group on Nonlinear Partial Differential EquationsRevista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie a-Matematicas, 116(4). ISSN: 1578-7303
- J. C. Sabina de Lis; S. Segura de León(2022)p-Laplacian diffusion coupled to logistic reaction: asymptotic behavior as p goes to 1.Annali di Matematica Pura ed Applicata, 201(5), pp. 2197 - 2240. ISSN: 0373-3114
- J. C. Sabina de Lis; S. Segura de León(2022)Research Group on Nonlinear Partial Differential EquationsRicerche di Matematica, 71(2), pp. 529 - 547. ISSN: 0035-5038
- A. Molino Salas; S. Segura de León(2022)Research Group on Nonlinear Partial Differential EquationsMatemática Contemporânea, 52, pp. 71 - 86. ISSN: 0103-9059
- J.C. Ortiz; M.T.O. Pimenta; S. Segura de León(2023)Research Group on Nonlinear Partial Differential EquationsJournal of Mathematical Analysis and Applications, 525(2). ISSN: 0022-247X
- F. Della Pietra; F. Oliva; S. Segura de León(2024)Research Group on Nonlinear Partial Differential EquationsProceedings of the Royal Society of Edinburgh Section A-Mathematics, 154(1), pp. 105 - 130. ISSN: 0308-2105
- F. Della Pietra; F. Oliva; S. Segura de León(2024)Research Group on Nonlinear Partial Differential EquationsAdvances In Nonlinear Analysis, 13. ISSN: 2191-9496
- F. Oliva; F. Petitta; S. Segura de León(2024)Research Group on Nonlinear Partial Differential EquationsNodea-Nonlinear Differential Equations and Applications, 31. ISSN: 1021-9722
- J. C. Sabina de Lis; S. Segura de León(2024)Higher Robin eigenvalues for the p-Laplacian as p goes to 1.Calculus of Variations and Partial Differential Equations, 63(7). ISSN: 0944-2669
- A. Ferone; A. Mercaldo; S. Segura de León(2025)Research Group on Nonlinear Partial Differential EquationsAdvances In Differential Equations, 30(9-10), pp. 635 - 670. ISSN: 1079-9389
- J. C. Sabina de Lis; S. Segura de León(2026)Research Group on Nonlinear Partial Differential EquationsJournal of Differential Equations, 455. ISSN: 0022-0396

CNAE

University education

Associated structure

Mathematical Analysis

www.uv.es/anamat

dep.analisi.matematica@uv.es

Contact group details

Research Group on Nonlinear Partial Differential Equations (EDPNOL)

Burjassot/Paterna Campus

C/ Dr. Moliner, 50

46100 Burjassot (Valencia)

+34 963 544 721

Geolocation

jose.m.mazon@uv.es

Contact people

MAZON RUIZ, JOSE M
PDI-Emerit/a Universitat

View details

Research Group on Nonlinear Partial Differential Equations - EDPNOL