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Silvia Frassu

Publications and source records attributed to Silvia Frassu.

At least 19 recordsLinked to original sources
arXiv2026

Global boundedness of a two-species attraction-attraction chemotaxis model with bilinear boundary influx

Since its introduction, the Keller--Segel model has become a cornerstone in the mathematical theory of chemotaxis and it has generated extensive analytical activity. Most studies consider homogeneous Neumann boundary conditions, which ensure mass conservation and simplify the qualitative analysis of solutions. To the best of the authors' knowledge, at present chemotaxis models incorporating boundary conditions that generate inward fluxes have only been studied in two recent papers, and we believe that this topic deserves and it may attract further mathematical attention. In this sense, in the present paper we investigate a two-species chemotaxis system with positive total flux. The model consists of two interacting populations, $u$ and $w$, coupled through elliptic/parabolic chemical signals $v$ and $z$, and subject to Robin-type boundary conditions allowing inward fluxes that depend on the product of the cellular and chemical densities. Unlike the classical conservative setting, the total mass is not preserved and it exhibits quadratic growth in time, exactly in line with one of the investigations above mentioned and dealing with a single-species taxis model. We show that, within the considered framework, standard logistic damping is not sufficient to compensate for the mass increase induced by the positive boundary flux. To restore control of the dynamics, stronger dissipative mechanisms involving gradient-dependent damping terms are required. Under suitable assumptions, we establish the global existence and boundedness of classical solutions in the presence of logistic-gradient damping.

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arXiv2025

Global dynamics of chemotaxis-consumption systems with oppositely acting nonlocal terms

This paper studies a chemotaxis system where cells move in response to a chemical signal within a confined habitat. The model includes external source terms that combine local and nonlocal growth with dampening effects. The main focus is on conditions under which solutions exist for all time and remain uniformly bounded, preventing cell aggregation. Two types of source terms are considered. In the first case, the structure of the source term ensures that the total cell mass remains controlled over time. In the second case, this mass control is not guaranteed, which can lead to different dynamic behaviors. The results extend previous studies that examined similar systems but with more specific source terms and slightly different chemical dynamics. This work highlights how variations in the reaction terms influence the long-term behavior of the system.

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arXiv2025

Chemotaxis models with mixed mechanisms: boundedness in growth-dominated regimes

We study a chemotaxis-growth system with nonlinear local and nonlocal reactions and gradient-dependent damping. Under suitable conditions on the system parameters and spatial dimension, we prove that solutions exist globally in time and remain uniformly bounded. Unlike classical cases, when local growth dominates, mass control is not automatic. To address this, we use a two-step approach: first ensuring bounded total mass, then establishing full uniform boundedness. The results highlight how chemotaxis, damping, and nonlocal effects interact to prevent blow-up in structured models.

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arXiv2025

To what extent does the consideration of positive total flux influence the dynamics of Keller-Segel-type models?

Since the introduction of the Keller-Segel model in 1970 to describe chemotaxis (the interactions between cell distributions u and chemical distributions v), there has been a significant proliferation of research articles exploring various extensions and modifications of this model within the scientific community. From a technical standpoint, the totality of results concerning these variants are characterized by the assumption that the total flux, involving both distributions, of the model under consideration is zero. This research aims to present a novel perspective by focusing on models with a positive total flux. Specifically, by employing Robin-type boundary conditions for u and v, we seek to gain insights into the interactions between cells and their environment, uncovering important dynamics such as how variations in boundary conditions influence chemotactic behavior. In particular, the choice of the boundary conditions is motivated by real-world phenomena and by the fact that the related analysis reveals some interesting properties of the system.

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arXiv2024

Dissipation through combinations of nonlocal and gradient nonlinearities in chemotaxis models

This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two densities is studied in bounded and impenetrable regions. In particular, it is seen that no gathering effect for the cells can appear in time provided that the damping impacts are sufficiently strong.

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arXiv2023

Uniform-in-time boundedness in a class of local and nonlocal nonlinear attraction-repulsion chemotaxis models with logistics

This article deals with a class of chemotaxis systems describing mechanisms from mathematical biology. In the specific, for a rather general class of attraction-repulsion models, with nonlinear productions, diffusion, sensitivities and logistic term, we are interested in deriving interplays on the parameters involved in the problem capable to ensure globality and boundedness of related solutions. This project is precisely contextualized in the frame of a series of results dealing with local and nonlocal, and linear and nonlinear, attraction-repulsion chemotaxis systems. For these problems, rooms of improvements are still open; in this sense, this research exactly enhances and extends already known analyses in the literature. More specifically, a direct comparison with [Jiao, Jadlovská, Li, Nonlinear Anal. Real World Appl., 2023; Ren, Liu, Math. Models Methods Appl. Sci., 2020; Chiyo, Yokota, Z. Angew. Math. Phys., 2022; Columbu, Frassu, Viglialoro, Appl. Anal., 2023] is carried out.

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arXiv2023

Boundedness through nonlocal dampening effects in a fully parabolic chemotaxis model with sub and superquadratic growth

This work deals with a chemotaxis model where an external source involving a sub and superquadratic growth effect contrasted by nonlocal dampening reaction influences the motion of a cell density attracted by a chemical signal. We study the mechanism of the two densities once their initial configurations are fixed in bounded impenetrable regions; in the specific, we establish that no gathering effect for the cells can appear in time provided that the dampening effect is strong enough.

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arXiv2023

Properties of given and detected unbounded solutions to a class of chemotaxis models

This paper deals with unbounded solutions to a class of chemotaxis systems. In particular, for a rather general attraction-repulsion model, with nonlinear productions, diffusion, sensitivities and logistic term, we detect Lebesgue spaces where given unbounded solutions blow-up also in the corresponding norms of those spaces; subsequently, estimates for the blow-up time are established. Finally, for a simplified version of the model, some blow-up criteria are proved.

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arXiv2022

Bifurcation-type results for the fractional p-Laplacian with parametric nonlinear reaction

We study a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction, which depends on a positive parameter. The reaction is assumed to be (p-1)-sublinear near the origin and (p-1)-superlinear at infinity (including the concave-convex case). Following a variational approach based on a combination of critical point theory and suitable truncation techniques, we prove a bifurcation-type result for the existence of positive solutions.

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arXiv2022

Combining effects ensuring boundedness in an attraction-repulsion chemotaxis model with production and consumption

This paper is framed in a series of studies on attraction-repulsion chemotaxis models combining different effects: nonlinear diffusion and sensitivities and logistic sources, for the dynamics of the cell density, and consumption and/or production impacts, for those of the chemicals. In particular, herein we focus on the situation where the signal responsible of gathering tendencies for the particles' distribution is produced, while the opposite counterpart is consumed. In such a sense, this research complements two recent results, where the chemicals evolve according to different laws.

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arXiv2021

Improvements and generalizations of results concerning attraction-repulsion chemotaxis models

We enter the details of two recent articles concerning as many chemotaxis models, one nonlinear and the other linear, and both with produced chemoattractant and saturated chemorepellent. These works, when properly analyzed, leave open room for some improvement of their results. We generalize the outcomes of the mentioned articles, establish other statements and put all the claims together; in particular, we select the sharpest ones and schematize them. Moreover, we complement our research also when logistic sources are considered in the overall study.

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arXiv2021

Five solutions for the fractional p-Laplacian with noncoercive energy

We deal with a Dirichlet problem driven by the degenerate fractional p-Laplacian and involving a nonlinear reaction which satisfies, among other hypotheses, a (p-1)-linear growth at infinity with non-resonance above the first eigenvalue. The energy functional governing the problem is thus noncoercive. Thus we focus on the behavior of the reaction near the origin, assuming that it has a (p-1)-sublinear growth at zero, vanishes at three points, and satisfies a reverse Ambrosetti-Rabinowitz condition. Under such assumptions, by means of critical point theory and Morse theory, and using suitably truncated reactions, we show the existence of five nontrivial solutions: two positive, two negative, and one nodal.

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arXiv2021

On some sharper boundedness conditions in the higher-dimensional chemotaxis-consumption model

For the classical zero-flux chemotaxis-consumption model \begin{equation*} u_t= Δu - χ\nabla \cdot (u \nabla v) \quad \textrm{and}\quad v_t=Δv- uv, \quad \text{ with } (x,t)\in Ω\times (0,T_{max}), \end{equation*} $Ω$ being a bounded and smooth domain of $\mathbb{R}^n$, $n\geq 3$, $χ$ some positive number and $T_{max} \in (0,\infty]$, the following was established in a paper by Tao: for every sufficiently regular initial data $u(x,0)=u_0(x)\geq 0$ and $v(x,0)=v_0(x) \geq 0$, there is $χ(\lVert v_0 \rVert_{L^\infty(Ω)})$ such that for all $0<χ\leq χ(\lVert v_0 \rVert_{L^\infty(Ω)})$, the initial-boundary value problem has a unique classical solution in $Ω\times (0,\infty)$ which is bounded. In this paper, whenever $n\geq 5$, we obtain the same claim for larger values of the constant $χ(\|v_0\|_{L^{\infty}(Ω)})$.

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arXiv2021

Multiple solutions for the fractional p-Laplacian with jumping reactions

We study a nonlinear elliptic equation driven by the degenerate fractional p-Laplacian, with Dirichlet type condition and a jumping reaction, i.e., (p-1)-linear both at infinity and at zero but with different slopes crossing the principal eigenvalue. Under two different sets of hypotheses, entailing different types of asymmetry, we prove the existence of at least two nontrivial solutions. Our method is based on degree theory for monotone operators and nonlinear fractional spectral theory.

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