The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the role of heterogeneity in equations and interactions in coupled systems. In this direction, we investigate three separate problems, each corresponding to a chapter of this thesis. The first problem addresses the evolution of a single population living in a periodic medium with a fast diffusion line; this corresponds to the study of a reaction-diffusion system with equations in different dimensions. We derive results on asymptotic behaviour through the study of some generalised principal eigenvalues. We find that the road has no impact on the survival chances of the population, despite the deleterious effect expected from fragmentation. The second investigation regards a model describing the competition between two populations in a situation of asymmetrically aggressive interactions; this consists of a system of two ODEs. The evolution progresses through two possible scenarios, where only one population survives. Then, the interpretation of one of the parameters as the aggressiveness of the attacker population naturally raises questions of controllability. We characterise the set of initial conditions leading to the victory of the attacker through a suitable (possibly time-dependant) strategy. The third and last part of this thesis analyses the time decay of some evolution equations with classical and fractional time derivatives. Depending on the type of derivative and some degree of non-degeneracy of the spatial operator, quantitative polynomial or exponential estimates are entailed.

EVOLUTION EQUATIONS WITH APPLICATIONS TO POPULATION DYNAMICS / E. Affili ; tutor: E. Valdinoci, L. Rossi ( Sorbonne Universite'). - : . Università degli Studi di Milano, 2021 Mar 11. ((33. ciclo, Anno Accademico 2020. [10.13130/affili-elisa_phd2021-03-11].

EVOLUTION EQUATIONS WITH APPLICATIONS TO POPULATION DYNAMICS

E. Affili
2021

Abstract

The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the role of heterogeneity in equations and interactions in coupled systems. In this direction, we investigate three separate problems, each corresponding to a chapter of this thesis. The first problem addresses the evolution of a single population living in a periodic medium with a fast diffusion line; this corresponds to the study of a reaction-diffusion system with equations in different dimensions. We derive results on asymptotic behaviour through the study of some generalised principal eigenvalues. We find that the road has no impact on the survival chances of the population, despite the deleterious effect expected from fragmentation. The second investigation regards a model describing the competition between two populations in a situation of asymmetrically aggressive interactions; this consists of a system of two ODEs. The evolution progresses through two possible scenarios, where only one population survives. Then, the interpretation of one of the parameters as the aggressiveness of the attacker population naturally raises questions of controllability. We characterise the set of initial conditions leading to the victory of the attacker through a suitable (possibly time-dependant) strategy. The third and last part of this thesis analyses the time decay of some evolution equations with classical and fractional time derivatives. Depending on the type of derivative and some degree of non-degeneracy of the spatial operator, quantitative polynomial or exponential estimates are entailed.
VALDINOCI, ENRICO
MASTROPIETRO, VIERI
population dynamics; biological mathematics; models for competing species; fractional derivatives; fast diffusion line; asymptotic behaviour
Settore MAT/05 - Analisi Matematica
EVOLUTION EQUATIONS WITH APPLICATIONS TO POPULATION DYNAMICS / E. Affili ; tutor: E. Valdinoci, L. Rossi ( Sorbonne Universite'). - : . Università degli Studi di Milano, 2021 Mar 11. ((33. ciclo, Anno Accademico 2020. [10.13130/affili-elisa_phd2021-03-11].
Doctoral Thesis
File in questo prodotto:
File Dimensione Formato  
phd_unimi_R12038.pdf

accesso aperto

Descrizione: Tesi di dottorato, introduzione + 3 capitoli
Tipologia: Tesi di dottorato completa
Dimensione 2.22 MB
Formato Adobe PDF
2.22 MB Adobe PDF Visualizza/Apri
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/820854
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact