# Nicola De NittiFriedrich-Alexander-University of Erlangen-Nürnberg | FAU · Department of Mathematics (Chair of Applied Analysis)

Nicola De Nitti

Master of Science

## About

17

Publications

1,921

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

15

Citations

Introduction

I'm a Ph.D. student in the Chair of Applied Analysis at Friedrich-Alexander-Universität Erlangen-Nürnberg.
My main research interests lie in the analysis and control of partial differential equations. More specifically, they include hyperbolic conservation laws, transport with rough velocity fields, flows on networks, (dissipative) hyperbolic PDEs, local and nonlocal degenerate (higher-order) parabolic PDEs, free boundary problems, variational and topological methods.

Additional affiliations

Education

March 2018 - March 2020

September 2014 - March 2018

## Publications

Publications (17)

We study the time-asymptotic behavior of linear hyperbolic systems under partial dissipation which is localized in suitable subsets of the domain. More precisely, we recover the classical decay rates of partially dissipative systems satisfying the stability condition (SK) with a time-delay depending only on the velocity of each component and the si...

We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing that the stream function associated to the magnetic field satisfies a simple drift–diffusion equation for which a...

For $s \in (0,1)$ and a bounded open set $\Omega \subset \mathbb R^N$ with $N > 2s$, we study the fractional Brezis--Nirenberg type minimization problem of finding $$ S(a) := \inf \frac{\int_{\mathbb R^N} |(-\Delta)^{s/2} u|^2 + \int_\Omega a u^2}{\left( \int_\Omega u^\frac{2N}{N-2s} \right)^\frac{N-2s}{N}}, $$ where the infimum is taken over all f...

We consider a class of nonlocal conservation laws with a second-order viscous regularization term which finds an application in modelling macroscopic traffic flow. The velocity function depends on a weighted average of the density ahead, where the averaging kernel is of exponential type. We show that, as the nonlocal impact and the viscosity parame...

We study the exact boundary controllability of a class of nonlocal conservation laws modeling traffic flow. The velocity of the macroscopic dynamics depends on a weighted average of the traffic density ahead and the averaging kernel is of exponential type. Under specific assumptions, we show that the boundary controls can be used to steer the syste...

We consider a degenerate nonlocal parabolic equation introduced to model hydraulic fractures, where the nonlocal operator is given by a fractional power of the Laplacian. Using a localized entropy estimate and a Stampacchia-type lemma, we establish a finite speed of propagation result and sufficient conditions (and lower bounds) for the waiting-tim...

We establish new Liouville-type theorems for the two-dimensional stationary magneto-hydrodynamic incompressible system assuming that the velocity and magnetic field have bounded Dirichlet integral. The key tool in our proof is observing that the stream function associated to the magnetic field satisfies a simple drift-diffusion equation for which a...

In this note, we extend the known results on the existence and uniqueness of weak solutions to conservation laws with nonlocal flux. In case the nonlocal term is given by a convolution γ * q, we weaken the standard assumption on the kernel γ ∈ L ∞ (0, T); W 1,∞ (R) to the substantially more general condition γ ∈ L ∞ ((0, T); BV (R)), which allows f...

We prove the convergence of the vanishing viscosity approximation for a class of \begin{document}$ 2\times2 $\end{document} systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows us to avoid the typical constraints on the total variation and the \begin{document}$ L^1 $\end{docum...

We deal with the problem of approximating a scalar conservation law by a conservation law with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential-type approximation of the Dirac distribution. This enables us to obtain a total variation bound on the nonlocal term. By using this, we prove that the (unique) weak solu...

Preprint available at https://cvgmt.sns.it/paper/4858/

We prove the convergence of the vanishing viscosity approximation for a class of $2 \times 2$ systems of conservation laws, which includes a model of traffic flow in congested regimes. The structure of the system allows to avoid the typical constraints on the total variation and the $L^1$ norm of the initial data. The key tool is the compensated co...

We consider a class of nonlocal conservation laws with a second-order viscous regularization term which finds an application in modelling macroscopic traffic flow. The velocity function depends on a weighted average of the density ahead, where the averaging kernel is of exponential type. We show that, as the nonlocal reach and the viscosity paramet...

We study the exact boundary controllability of a class of nonlocal conservation laws modeling traffic flow. The velocity of the macroscopic dynamics depends on a weighted average of the traffic density ahead and the averaging kernel is of exponential type. Under specific assumptions, we show that the boundary controls can be used to steer the syste...

We prove existence of solutions to a conservation law with nonlocal discontinuous flux modeling material flow on a conveyor belt. The discontinuity is with respect to the unknown function and arises in a dynamic velocity field which is active only at high densities and takes into account the effect of colliding parts though the nonlocal operator. T...

We establish sharp criteria for the instantaneous propagation of free boundaries in solutions to the thin-film equation. The criteria are formulated in terms of the initial distribution of mass (as opposed to previous almost-optimal results), reflecting the fact that mass is a locally conserved quantity for the thin-film equation. In the regime of...

## Projects

Projects (5)

We apply variational and topological methods to the study of (nonlocal) nonlinear problems.

Analysis of partial differential equations arising in fluid mechanics

We study hyperbolic conservation laws arising in models of traffic flow or gas transport.