Noha Khattabi - Academia.edu (original) (raw)

Papers by Noha Khattabi

Research paper thumbnail of Mathematical modelling of the anaerobic digestion process with acidogenic and methanogenic biomasses

Authorea (Authorea), Apr 14, 2024

Research paper thumbnail of Mathematical model of anaerobic digestion with hydrolytic process by means of leachate recirculation in landfills

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of Solutions comparison for non-monotone dynamical systems

We give conditions for a non-monotone system to preserve the usual vector order of solutions for ... more We give conditions for a non-monotone system to preserve the usual vector order of solutions for a subset of initial conditions. Our approach consists of separating terms that meet Kamke's sign condition from other ones in the dynamics, and considering Picard iterations. These conditions amount for the dynamics to preserve a partial order, which is not necessarily induced by a cone. Examples illustrate the results.

Research paper thumbnail of Multiple solutions of problems with nonlinear first-order differential operators

Journal of Fixed Point Theory and Applications, 2015

In this paper, we establish the existence of solutions to firstorder differential equations with ... more In this paper, we establish the existence of solutions to firstorder differential equations with nonlinear differential operators satisfying the periodic boundary value or the initial value conditions. Notions of upper and lower solutions are introduced. Multiplicity results are also presented.

Research paper thumbnail of Systems of Stieltjes differential equations and application to a predator-prey model of an exploited fishery

Discrete and Continuous Dynamical Systems

Research paper thumbnail of Mathematical analysis of an anaerobic co‐digestion model with preference function and mortality

Mathematical Methods in The Applied Sciences, Feb 15, 2023

Research paper thumbnail of Existence and multiplicity results for first-order Stieltjes differential equations

Advanced Nonlinear Studies, 2022

In this article, we establish existence and multiplicity results for first-order Stieltjes differ... more In this article, we establish existence and multiplicity results for first-order Stieltjes differential equations satisfying a periodic boundary condition or an initial value condition. No monotonicity condition involving the right-hand side f is imposed at the discontinuity points of the derivator g. Our results rely on the fixed point index theory and new notions of strict lower and upper solutions. An application to a population model with an extreme event is presented to study the persistence of a species.

Research paper thumbnail of Time series analysis for waste quantities prediction in a north African city

Proceedings of the 2017 International Conference on Smart Digital Environment, 2017

Municipal Solid Waste (MSW) Generation is an important variable in waste management and used to s... more Municipal Solid Waste (MSW) Generation is an important variable in waste management and used to support decision makers and planners to do short and medium term management strategies. The main objective of this paper is to assist decision makers in this process using time series analysis in a Moroccan city with a high urbanization and economic growth. For this, we study, select and evaluate waste production model using Box-Jenkins Methodology. The accurate SARIMA (Seasonal Auto-Regressive, Integrated, Moving Average) model is selected for monthly waste generation in Kenitra, Morocco, based on data from January 2005 to December 2015. The model obtained shows the presence of seasonality in monthly waste generation in this city. This model also conforms that monthly production of waste in the city of Kenitra, Morocco, depends on that of the previous month but also on the same month of the previous season. Accuracy of predictions is measured by Mean Absolute Percentage Errors (MAPE) whi...

Research paper thumbnail of Bioeconomic modeling of household waste recovery

The ecological consciousness has driven developed societies to explore alternatives to the growin... more The ecological consciousness has driven developed societies to explore alternatives to the growing need for energy and the consequent increase in waste production. The adjustment towards the waste recovery and their transformation into energy, by various processes, is then necessary. However, so far the domain has not benefited much from a mathematical modeling approach.

Research paper thumbnail of Problèmes périodiques du second ordre à croissance au plus linéaire

Topological Methods in Nonlinear Analysis, 1995

Research paper thumbnail of Multiple solutions of boundary value problems with ϕ-Laplacian operators and under a Wintner-Nagumo growth condition

Boundary Value Problems, 2013

In this paper, we establish the existence of multiple solutions to second-order differential equa... more In this paper, we establish the existence of multiple solutions to second-order differential equations with ϕ-Laplacian satisfying periodic, Dirichlet or Neumann boundary conditions. The right-hand side is a Carathéodory function satisfying a growth condition of Wintner-Nagumo type. The existence of upper and lower solutions is assumed. The proofs rely on the fixed point index theory. MSC: 34B15, 34C25, 47H10, 37C25, 47H11.

Research paper thumbnail of Mathematical model of anaerobic digestion with leachate recirculation

Le Centre pour la Communication Scientifique Directe - HAL - Inria, Oct 4, 2022

Landfilled biodegradable materials are subject to biological evolution, namely biodegradation or ... more Landfilled biodegradable materials are subject to biological evolution, namely biodegradation or digestion, under the action of aerobic bacteria and further anaerobic bacteria. In the absence of special provisions, the liquid flowing through the mass of waste produces leachate, being charged with chemical or biological substances. Therefore, the mathematical modeling is of great interest for making decisions in the field of waste management since it makes possible to predict the behavior of the various complex systems underlying the management of waste. The analysis of the dynamics of the model considered in our work describes the process of anaerobic biodegradation with leachate reinjection, and allows us to predict the amount of biogas produced in the long term. The system admits an infinity of non hyperbolic equilibria but we are able to describe the asymptotic behavior of the solutions depending on the initial condition. Thanks to this model, we can highlight the influence of the leachate recirculation on the production of biogas, with the help of numerical simulations. This recirculation could be a part of the sustainable solutions adapted by recent technologies for the treatment of waste, not only to optimize the total production of biogas, but also to obtain a good quality of the outgoing liquid to meet the discharge standards.

Research paper thumbnail of Mathematical modelling of the anaerobic digestion process with acidogenic and methanogenic biomasses

Authorea (Authorea), Apr 14, 2024

Research paper thumbnail of Mathematical model of anaerobic digestion with hydrolytic process by means of leachate recirculation in landfills

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of Solutions comparison for non-monotone dynamical systems

We give conditions for a non-monotone system to preserve the usual vector order of solutions for ... more We give conditions for a non-monotone system to preserve the usual vector order of solutions for a subset of initial conditions. Our approach consists of separating terms that meet Kamke's sign condition from other ones in the dynamics, and considering Picard iterations. These conditions amount for the dynamics to preserve a partial order, which is not necessarily induced by a cone. Examples illustrate the results.

Research paper thumbnail of Multiple solutions of problems with nonlinear first-order differential operators

Journal of Fixed Point Theory and Applications, 2015

In this paper, we establish the existence of solutions to firstorder differential equations with ... more In this paper, we establish the existence of solutions to firstorder differential equations with nonlinear differential operators satisfying the periodic boundary value or the initial value conditions. Notions of upper and lower solutions are introduced. Multiplicity results are also presented.

Research paper thumbnail of Systems of Stieltjes differential equations and application to a predator-prey model of an exploited fishery

Discrete and Continuous Dynamical Systems

Research paper thumbnail of Mathematical analysis of an anaerobic co‐digestion model with preference function and mortality

Mathematical Methods in The Applied Sciences, Feb 15, 2023

Research paper thumbnail of Existence and multiplicity results for first-order Stieltjes differential equations

Advanced Nonlinear Studies, 2022

In this article, we establish existence and multiplicity results for first-order Stieltjes differ... more In this article, we establish existence and multiplicity results for first-order Stieltjes differential equations satisfying a periodic boundary condition or an initial value condition. No monotonicity condition involving the right-hand side f is imposed at the discontinuity points of the derivator g. Our results rely on the fixed point index theory and new notions of strict lower and upper solutions. An application to a population model with an extreme event is presented to study the persistence of a species.

Research paper thumbnail of Time series analysis for waste quantities prediction in a north African city

Proceedings of the 2017 International Conference on Smart Digital Environment, 2017

Municipal Solid Waste (MSW) Generation is an important variable in waste management and used to s... more Municipal Solid Waste (MSW) Generation is an important variable in waste management and used to support decision makers and planners to do short and medium term management strategies. The main objective of this paper is to assist decision makers in this process using time series analysis in a Moroccan city with a high urbanization and economic growth. For this, we study, select and evaluate waste production model using Box-Jenkins Methodology. The accurate SARIMA (Seasonal Auto-Regressive, Integrated, Moving Average) model is selected for monthly waste generation in Kenitra, Morocco, based on data from January 2005 to December 2015. The model obtained shows the presence of seasonality in monthly waste generation in this city. This model also conforms that monthly production of waste in the city of Kenitra, Morocco, depends on that of the previous month but also on the same month of the previous season. Accuracy of predictions is measured by Mean Absolute Percentage Errors (MAPE) whi...

Research paper thumbnail of Bioeconomic modeling of household waste recovery

The ecological consciousness has driven developed societies to explore alternatives to the growin... more The ecological consciousness has driven developed societies to explore alternatives to the growing need for energy and the consequent increase in waste production. The adjustment towards the waste recovery and their transformation into energy, by various processes, is then necessary. However, so far the domain has not benefited much from a mathematical modeling approach.

Research paper thumbnail of Problèmes périodiques du second ordre à croissance au plus linéaire

Topological Methods in Nonlinear Analysis, 1995

Research paper thumbnail of Multiple solutions of boundary value problems with ϕ-Laplacian operators and under a Wintner-Nagumo growth condition

Boundary Value Problems, 2013

In this paper, we establish the existence of multiple solutions to second-order differential equa... more In this paper, we establish the existence of multiple solutions to second-order differential equations with ϕ-Laplacian satisfying periodic, Dirichlet or Neumann boundary conditions. The right-hand side is a Carathéodory function satisfying a growth condition of Wintner-Nagumo type. The existence of upper and lower solutions is assumed. The proofs rely on the fixed point index theory. MSC: 34B15, 34C25, 47H10, 37C25, 47H11.

Research paper thumbnail of Mathematical model of anaerobic digestion with leachate recirculation

Le Centre pour la Communication Scientifique Directe - HAL - Inria, Oct 4, 2022

Landfilled biodegradable materials are subject to biological evolution, namely biodegradation or ... more Landfilled biodegradable materials are subject to biological evolution, namely biodegradation or digestion, under the action of aerobic bacteria and further anaerobic bacteria. In the absence of special provisions, the liquid flowing through the mass of waste produces leachate, being charged with chemical or biological substances. Therefore, the mathematical modeling is of great interest for making decisions in the field of waste management since it makes possible to predict the behavior of the various complex systems underlying the management of waste. The analysis of the dynamics of the model considered in our work describes the process of anaerobic biodegradation with leachate reinjection, and allows us to predict the amount of biogas produced in the long term. The system admits an infinity of non hyperbolic equilibria but we are able to describe the asymptotic behavior of the solutions depending on the initial condition. Thanks to this model, we can highlight the influence of the leachate recirculation on the production of biogas, with the help of numerical simulations. This recirculation could be a part of the sustainable solutions adapted by recent technologies for the treatment of waste, not only to optimize the total production of biogas, but also to obtain a good quality of the outgoing liquid to meet the discharge standards.