Postdoctoral Researcher
jean-daniel.djida@fau.de
Room 03.316 | Friedrich-Alexander-Universität Erlangen-Nürnberg. FAU DCN-AvH Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship.
+49 9131 85-67171
My research sits at the crossroads of model-driven and data-driven approaches, where mathematical rigor meets real-world applications.
– Mathematical Tools for PDE Analysis: My work in this domain centers around the study and application of partial differential equations (PDEs), with a special focus on nonlinear phenomena and systems. Key areas of interest include non-linear drift-diffusion equations, control theory, mean field equations, many-particle systems, gradient flows, and the domination of semigroups. I also explore advanced techniques like entropy methods, optimal transport, functional inequalities, and the scaling behaviors of parabolic and hyperbolic systems. Additionally, I am particularly engaged in hypocoercivity and the role of diffusive models in mathematical biology.
– Mathematical Tools for Data Analysis: I am equally passionate about the development of rigorous mathematical frameworks for data analysis, especially within the contexts of inverse problems, Bayesian inference, and machine learning. My research delves into unsupervised and semi-supervised learning methodologies, with a strong emphasis on data clustering, classification, uncertainty quantification, and consistency analysis.
I believe that the relationship between mathematics and its applications is symbiotic: while mathematical analysis can significantly enhance our understanding of real-world problems, the challenges posed by these applications often lead to the discovery of novel mathematical insights. This reciprocity fuels my interest in leveraging PDE techniques to address modeling questions across a wide spectrum of scales, disciplines, and applications. By engaging in this continuous feedback loop, I aim to push the boundaries of both applied and theoretical mathematics, fostering innovation in seemingly unrelated fields.
PhD Thesis: Some nonlocal operators in porous medium equations: the extension problem and regularity theory (2019)
Teaching
• WS 24/25: Mathematics for Engineers III
• SS 23/24: Mathematics for Engineers II
• WS 23/24: Machine Learning in Finance
My posts
Analysis of a local-nonlocal polymer chain model
Publications
2024
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Domination of semigroups generated by regular forms
In: Proceedings of the American Mathematical Society (2024)
ISSN: 0002-9939
DOI: 10.1090/proc/16702
URL: https://www.ams.org/journals/proc/0000-000-00/S0002-9939-2024-16702-2/
BibTeX: Download - , , :
On the fractional Laplacian of a function with respect to another function
In: Mathematical Methods in the Applied Sciences (2024)
ISSN: 0170-4214
DOI: 10.1002/mma.10256
BibTeX: Download
2022
- , , :
Nonlocal complement value problem for a global in time parabolic equation
In: Journal of Elliptic and Parabolic Equations 8 (2022), p. 767-789
ISSN: 2296-9020
DOI: 10.1007/s41808-022-00175-8
BibTeX: Download - , , :
OPTIMAL CONTROL OF MIXED LOCAL-NONLOCAL PARABOLIC PDE WITH SINGULAR BOUNDARY-EXTERIOR DATA
In: Evolution Equations and Control Theory 11 (2022), p. 2129-2163
ISSN: 2163-2480
DOI: 10.3934/eect.2022015
BibTeX: Download
2021
- Fernandez A., Djida J.D.:
Fractional differential relations for the Lerch zeta function
In: Archiv der Mathematik 117 (2021), p. 515-527
ISSN: 0003-889X
DOI: 10.1007/s00013-021-01654-5
BibTeX: Download - Oumarou C.M.S., Fahad H.M., Djida J.D., Fernandez A.:
On fractional calculus with analytic kernels with respect to functions
In: Computational and Applied Mathematics 40 (2021), Article No.: 244
ISSN: 0101-8205
DOI: 10.1007/s40314-021-01622-3
BibTeX: Download
2020
- Djida J., Nieto J., Area I.:
Parabolic problem with fractional time derivative with nonlocal and nonsingular Mittag-leffler kernel
In: Discrete and Continuous Dynamical Systems 13 (2020), p. 609-627
ISSN: 1078-0947
DOI: 10.3934/dcdss.2020033
BibTeX: Download - Djida J.D., Fernandez A., Area I.:
Well-posedness results for fractional semi-linear wave equations
In: Discrete and Continuous Dynamical Systems-Series B 25 (2020), p. 569-597
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2019255
BibTeX: Download
2019
- Feulefack P.A., Djida J.D., Abdon A.:
A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative
In: Discrete and Continuous Dynamical Systems-Series B 24 (2019), p. 3227-3247
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2018317
BibTeX: Download - Djida J.D., Nieto J.J., Area I.:
Nonlocal time-porous medium equation: Weak solutions and finite speed of propagation
In: Discrete and Continuous Dynamical Systems-Series B 24 (2019), p. 4031-4053
ISSN: 1531-3492
DOI: 10.3934/dcdsb.2019049
BibTeX: Download - Djida J., Nieto J., Area I.:
Nonlocal time porous medium equation with fractional time derivative
In: Revista Matematica Complutense 32 (2019), p. 273-304
ISSN: 1139-1138
DOI: 10.1007/s13163-018-0287-0
BibTeX: Download - Djida J., Nieto J., Area I.:
Nonlocal time porous medium equation with fractional time derivative
In: Revista Matematica Complutense 32 (2019), p. 273-304
ISSN: 1139-1138
DOI: 10.1007/s13163-018-0287-0
BibTeX: Download - Djida J.D., Mophou G., Area I.:
Optimal Control of Diffusion Equation with Fractional Time Derivative with Nonlocal and Nonsingular Mittag-Leffler Kernel
In: Journal of Nonlinear Analysis and Optimization : Theory & Applications 182 (2019), p. 540-557
ISSN: 1906-9685
DOI: 10.1007/s10957-018-1305-6
BibTeX: Download
2018
- Djida J.D., Fernandez A.:
Interior regularity estimates for a degenerate elliptic equation with mixed boundary conditions
In: Axioms 7 (2018), Article No.: 65
ISSN: 2075-1680
DOI: 10.3390/axioms7030065
BibTeX: Download
2017
- Djida J., Atangana A.:
More generalized groundwater model with space-time caputo Fabrizio fractional differentiation
In: Numerical Methods For Partial Differential Equations 33 (2017), p. 1616-1627
ISSN: 0749-159X
DOI: 10.1002/num.22156
BibTeX: Download - Djida J.D., Atangana A., Area I.:
Numerical Computation of a Fractional Derivative with Non-Local and Non-Singular Kernel
In: Mathematical Modelling of Natural Phenomena 12 (2017), p. 4-13
ISSN: 0973-5348
DOI: 10.1051/mmnp/201712302
BibTeX: Download
2015
- Rigatos G.G., Rigatou E.G., Djida J.D.:
Change detection in the dynamics of an intracellular protein synthesis model using nonlinear kalman filtering
In: Mathematical Biosciences and Engineering 12 (2015), p. 1017-1035
ISSN: 1547-1063
DOI: 10.3934/mbe.2015.12.1017
BibTeX: Download - Rigatos G., Rigatou E., Djida J.D.:
Detection of parametric changes in the Peyrard-Bishop- Dauxois model of DNA using nonlinear Kalman filtering
In: Journal of Biological Physics 41 (2015), p. 59-83
ISSN: 0092-0606
DOI: 10.1007/s10867-014-9366-8
BibTeX: Download - Area I., Djida J.D., Losada J., Nieto J.J.:
On Fractional Orthonormal Polynomials of a Discrete Variable
In: Discrete Dynamics in Nature and Society 2015 (2015), Article No.: 141325
ISSN: 1026-0226
DOI: 10.1155/2015/141325
BibTeX: Download
