Elisabetta Brocchieri

Universitätsassistentin

equivalent to non-tenured Assistant Professor

About me

Since March 2023, I am a non-tenured Assistant Professor at the University of Graz in the Applied Analysis Group, led by Klemens Fellner.

I achieved my PhD in Applied Mathematics on February 2023, jointly with Université Paris-Saclay and Sapienza, Università di Roma, under the supervision of L. Corrias (Uni Évry), L. Desvillettes (Uni Paris Cité) and E. Montefusco (Sapienza, Uni Roma).

A copy of my thesis can be found here.

My research interests focus on reaction cross-diffusion models arising from biology and ecology. I study these models from an analytical point of view by investigating the existence and regularity of solutions and the stability of the equilibria.

Research interests

Cross-diffusion systems;
Existence, uniqueness and regularity of solutions;
Rigorous derivation by fast reaction-diffusion systems;
Entropy, duality and fixed point methods;
Pattern formation: Turing instability;
Stability analysis of spatially heterogeneous equilibria.

Curriculum vitae

03/2023 - present: non tenured Assistant Professor - Postdoctoral researcher, Applied Analysis Group, University of Graz;
11/2019 - 02/2023: International PhD in Applied Mathematics, jointly with Paris Saclay and Sapienza;
10/2017 - 10/2019: Master in Mathematics (Sapienza, University of Rome);
09/2018 - 06/2019: Erasmus grant (IMO, Paris Saclay, Orsay);
10/2014 - 07/2017: Bachelor in Mathematics (Sapienza, University of Rome);
11/1995: Born in Rome (Italy).

One page CV (EN)

(last update March, 2025)

Publications

E. Brocchieri, C. Soresina. Cross-diffusion and fast-reaction in pattern formation: a structural analysis. 2026 preprint HAL/arXiv.
E. Brocchieri, L. Corrias. On a class of triangular cross-diffusion systems and its fast reaction approximation. 2025 preprint HAL/arXiv.
E. Brocchieri, L. Desvillettes, H. Dietert. Study of a class of triangular starvation driven cross-diffusion systems. 2024, Ricerche di Matematica.
E. Brocchieri, L. Corrias, H. Dietert, Y.-J. Kim. Evolution of dietary diversity and a starvation driven cross-diffusion system as its singular limit. 2021, J. Math. Biol.

Miscellaneous

E. Brocchieri. Evolutionary dynamics of populations structured by dietary diversity and starvation: cross-diffusion systems. 2023, PhD Thesis.

In preparation

E. Brocchieri, S. Buccheri. Well-posedness of a nonlinear parabolic equation with a Hölder continuous first order term.
E. Brocchieri, F. Ferraresso, F. Gladiali. Well-posedness of a model for the Alzheimer disease progression with chemotactic term.
E. Brocchieri, C. Reisch. Turing instability driven by a class of non local cross-diffusion systems.

Mentoring & Teaching

University of Graz - 03.2026: Supervision of B.Sc. thesis: Ms. L. List.

University of Graz - 12.2024: Co-supervision with C. Soresina of B.Sc. thesis: Ms. B. Horvath.

University of Graz
- 2025 - 2026: (106 hours)
  - - - Lecture course: Modelling in natural science. Master in Mathematics. Summer semester.
        Exercise course: Modelling in natural science. Master in Mathematics. Summer semester.
        Exercise course: Differential equations. Bachelor Lehramt. Winter semester.
        Seminar course: Mathematical Seminar. Master Lehramt. Winter semester.
- 2024 - 2025: (112 hours)
  - - - Lecture course: Modelling in natural science. Master in Mathematics. Summer semester.
        Exercise course: Modelling in natural science. Master in Mathematics. Summer semester.
        Exercise course: Modelling. Master Lehramt. Winter semester.
        Exercise course: Differential equations. Bachelor Lehramt. Winter semester.
- 2023 - 2024: (93 hours)
  - - - Lecture course: Modelling in natural science. Master in Mathematics. Summer semester.
        Exercise course: Modelling, exercise course. Bachelor in Mathematics. Summer semester.
        Exercise course: Advanced Functional Analysis. Master in Mathematics. Winter semester.
        Exercise course: Differential equations. Bachelor Lehramt. Winter semester.
Université d'Évry - Paris Saclay
- 2021 - 2022: (33 hours)
  - - - Exercise course: Analyse Mathématique 3. Bachelor in Économie et Gestion. Winter semester.
- 2020 - 2021: (60 hours)
  - - - Exercise course: Analyse Mathématique 3. Bachelor in Économie et Gestion. Winter semester.
        Exercise course: Langage Mathématique. Bachelor in Mathématiques et Informatique. Winter semester.