### Welcome

Since November 2021, I am a Postdoc researcher at UNIMORE - Department of Sciences and Method for Engineering, Modena and Reggio Emilia (Italy).
[Supervisor: Prof. Luisa Malaguti]

Previously, I was a Postdoc researcher at CNRS - CAMS, Paris (France) [Supervisor: Prof. Henri Berestycki]; at INdAM in the Departement of Mathematics and Geosciences at University of Trieste (Italy) [Supervisor: Prof. Pierpaolo Omari] and a Postdoc researcher at CMUP, Porto (Portugal) [Supervisor: Prof. Isabel S. Labouriau]. I was also a Visiting researcher at CMAF-CIO, University of Lisbon (Portugal).

### Research

Highlights & Events
• Equadiff15
Masaryk University, Brno (Czech Republic), 11–15 July 2022 (Co-organizer of a minisymposia). — Stay tuned
Works in Progress
• Nonregular wavefront solutions to reaction-convection equations with Perona-Malik diffusion, with Andrea Corli, and Luisa Malaguti.
• Reaction-diffusion equations with transmission conditions, with Henri Berestycki.
Preprints
• Stationary fronts and pulses for multistable equations with saturating diffusion, with Maurizio Garrione.
• Stability, bifurcations and hydra effects in an age-structured population model with threshold harvesting, with Eduardo Liz.

#### Topics

My research is driven in the area of nonlinear analysis concerning the theory of ordinary and partial differential equations and chaotic dynamical systems. I investigate solutions of boundary value problems associated with semilinear and quasilinear elliptic differential equations and wavefronts type solutions for reaction-diffusion equations. I am interested in population biology applications, and I deal with dynamical systems theory, topological and variational methods, and bifurcation techniques.

Keywords

#### Fundings

• Postdoc Fellowship from FSMP. Research project: "Reaction-Diffusion Equations in Population Genetics: a study of the influence of geographical barriers on traveling waves and non-constant stationary solutions".
• Postdoc Fellowship from INdAM (Istituto Nazionale di Alta Matematica). Research Project: "Problems in Population Dynamics: from Linear to Nonlinear Diffusion".

### Publications

Recent Publications
Wavefront solutions to reaction-convection equations with Perona-Malik diffusion.

Journal of Differential Equations, 2022, with Andrea Corli, and Luisa Malaguti.

We study a nonlinear reaction-convection equation with a degenerate diffusion of Perona-Malik’s type and a monostable reaction term. Under quite general assumptions, we show the presence of wavefront solutions and prove their main properties. In particular, such wavefronts exist for every speed in a closed half-line and we give estimates of the threshold speed. The wavefront profiles are also strictly monotone and their slopes are uniformly bounded by the critical values of the diffusion.

Extinction or coexistence in periodic Kolmogorov systems of competitive type.

Discrete Contin. Dyn. Syst., 2021 (to appear), with Isabel Coelho and Carlota Rebelo.

We study a periodic Kolmogorov system describing two species nonlinear competition. We discuss coexistence and extinction of one or both species, and describe the domain of attraction of nontrivial periodic solutions in the axes, under conditions that generalise Gopalsamy conditions. Finally, we apply our results to a model of microbial growth and to a model of phytoplankton competion under the effect of toxins.

On the number of positive solutions to an indefinite parameter-dependent Neumann problem.

Discrete Contin. Dyn. Syst., 2021 (to appear), with Guglielmo Feltrin and Andrea Tellini.

We study the second-order boundary value problem$\begin{cases}\, -u''=a_{\lambda,\mu}(t) \, u^{2}(1-u), & t\in(0,1), \\\, u'(0)=0, \quad u'(1)=0,\end{cases}$ where $$a_{\lambda,\mu}$$ is a step-wise indefinite weight function, precisely $$a_{\lambda,\mu}\equiv\lambda$$ in $$[0,\sigma]\cup[1-\sigma,1]$$ and $$a_{\lambda,\mu}\equiv-\mu$$ in $$(\sigma,1-\sigma)$$, for some $$\sigma\in\left(0,\frac{1}{2}\right)$$, with $$\lambda$$ and $$\mu$$ positive real parameters. We investigate the topological structure of the set of positive solutions which lie in $$(0,1)$$ as $$\lambda$$ and $$\mu$$ vary. Depending on $$\lambda$$ and based on a phase-plane analysis and on time-mapping estimates, our findings lead to three different (from the topological point of view) global bifurcation diagrams of the solutions in terms of the parameter $$\mu$$. Finally, for the first time in the literature, a qualitative bifurcation diagram concerning the number of solutions in the $$(\lambda,\mu)$$-plane is depicted. The analyzed Neumann problem has an application in the analysis of stationary solutions to reaction-diffusion equations in population genetics driven by migration and selection.

### Contact

#### Work Adress

Università degli Studi di Modena e Reggio Emilia (UNIMORE)
Dipartimento di Scienze e Metodi dell’Ingegneria
Via Università 4, 41121 Modena, Italy