Hamidou Touré - Academia.edu (original) (raw)

Papers by Hamidou Touré

Springer proceedings in mathematics & statistics, 2019

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost ... more This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D α t x(t) = Ax(t) + D α-1 t F(t, x(t)), t ∈ R, where 1 < α < 2, A is a linear densely defined operator of sectorial type of ω < 0 on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation.

Afrika Matematika, 2012

ABSTRACT

Comptes rendus de l' …, 1994

... Titre du document / Document title. COMPACT ATTRACTORS FOR REACTION-DIFFUSION EQUATIONS IN RN... more ... Titre du document / Document title. COMPACT ATTRACTORS FOR REACTION-DIFFUSION EQUATIONS IN RN. Auteur(s) / Author(s). FEIREISL E. ; LAURENCOT P. ; SIMONDON F. ; TOURE H. ; Revue / Journal Title. Comptes rendus de l&#x27;Académie des sciences. ...

Afrika Matematika, 2012

In this work, a Schaefer fixed-point theorem is used to investigate the existence of solutions fo... more In this work, a Schaefer fixed-point theorem is used to investigate the existence of solutions for first order impulsive functional differential with variable times.

Cubo (Temuco), 2014

Motivated by the recent works by the first and the second named authors, in this paper we introdu... more Motivated by the recent works by the first and the second named authors, in this paper we introduce the notion of doubly-weighted pseudo-almost periodicity (respectively, doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basic properties of these new spaces are studied. To illustrate our work, we study, under Acquistapace-Terreni conditions and exponential dichotomy, the existence of (µ, ν)pseudo almost periodic (respectively, (µ, ν)-pseudo almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces. A few illustrative examples will be discussed at the end of the paper. RESUMEN Motivado por los trabajos recientes del primer y segundo autor, en este artículo introducimos la noción de seudo-casi periodicidad con doble peso (seudo-casi automorfía con doble peso respectivamente) usando Teoría de la Medida. Se estudian las propiedades básicas de estos espacios nuevos. Para ilustrar nuestro trabajo, bajo las condiciones de Acquistapace-Terreni y dicotomía exponencial estudiamos la existencia de soluciones (respectivamente, (µ, ν) seudo-casi periódicas (µ, ν) seudo-casi automórficas) para algunas ecuaciones parciales de evolución autónomas en espacios de Banach. Algunos ejemplos ilustrativos se discutirán al final del artículo.

We show in this paper the continuous dependence of mild solutions of =a\bigl(u, arphi(u)_x\bigr)_... more We show in this paper the continuous dependence of mild solutions of =a\bigl(u, arphi(u)_x\bigr)_x+v$ on =]0,T[ imes I$ with respect to the open interval $.

Afrika Matematika, 2012

ABSTRACT

Nonlinear Analysis: Theory, Methods & Applications, 2012

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost ... more This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D α t x(t) = Ax(t) + D α-1 t F(t, x(t)), t ∈ R, where 1 < α < 2, A is a linear densely defined operator of sectorial type of ω < 0 on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation.

Nonlinear Analysis: Theory, Methods & Applications, 2009

In this work, we study the existence and regularity of solutions for some partial functional inte... more In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense of Grimmer [R. Grimmer, Resolvent operators for integral ...

Nonlinear Analysis: Theory, Methods & Applications, 2009

In this work, we establish several results about the existence and regularity of solutions for so... more In this work, we establish several results about the existence and regularity of solutions for some neutral partial di erential equations with nonlocal conditions. We assume that the linear part generates a strongly continuous semigroup on a general Banach space.

CLUVA (CLimate change and Urban Vulnerability in Africa; http://www.cluva.eu/) is a 3 years proje... more CLUVA (CLimate change and Urban Vulnerability in Africa; http://www.cluva.eu/) is a 3 years project, funded by the European Commission in 2010. Its main objective is the estimate of the impacts of climate changes in the next 40 years at urban scale in Africa. The mission of CLUVA is to develop methods and knowledge to assess risks cascading from climate-changes. It downscales IPCC climate projections to evaluate threats to selected African test cities; mainly floods, sea-level rise, droughts, heat waves and desertification. The project evaluates and links: social vulnerability; vulnerability of in-town ecosystems and urban-rural interfaces; vulnerability of urban built environment and lifelines; and related institutional and governance dimensions of adaptation. A multi-scale and multi-disciplinary quantitative, probabilistic, modelling is applied. CLUVA brings together climate experts, risk management experts, urban planners and social scientists with their African counterparts in a...

ABSTRACT The United Nations Convention to Combat Desertification (UNCCD) defines desertification ... more ABSTRACT The United Nations Convention to Combat Desertification (UNCCD) defines desertification as &quot;land degradation in arid, semi-arid and dry sub-humid areas resulting from various factors, including climatic variations and human activities&quot;. Desertification is regarded as one of the major global environmental problems of the 21st century and the African sub-Sahara is often quoted as the most seriously affected region with a significant loss of biological and economic productivity of the land. In this geographic area, desertification processes are usually generated by soil erosion due to climate characteristics and fluctuations, unsustainable land uses, overgrazing and inappropriate agricultural practices. Preventing desertification requires an improved understanding of its causes, impact, degree and association with climate, soil, water, land cover, socio-economic factors and their combined effects. The development of methodologies capable of managing large amounts of data in an integrated approach is needed because of the complexity and variety of forms of desertification processes. The study was carried out within the FP7-ENV-2010 CLUVA project (CLimate change and Urban Vulnerability in Africa), aimed to estimate the sensitivity to land degradation in the urban and peri-urban areas of both Ouagadougou (Burkina Faso) and Saint Louis (Senegal) cities. The approach was based on the implementation and adaptation of the modeling methodology developed within the MEDALUS project (MEditerranean Desertification and Land Use). The model is characterized by a multi-factor approach based on the assessment of both environmental quality indicators (climate, soil, vegetation) and anthropogenic factors (land management). The methodology is adaptable to the local conditions, considering that some key indicators can be operationally defined through the inclusion or exclusion of parameters and the scores assigned in order to match the specific relevance of the factors. All local data, arranged in a GIS environment, allowed the generation of maps identifying Environmentally Sensitive Areas (ESAs) and Indices of Environmental Sensitivity (ESAI). As expected, the results highlighted an overall high sensitivity to desertification. In Ouagadougou, the poorly vegetated peri-urban zone, affected by an increasing demographic pressure as the result of immigration from surrounding rural areas, was found as the most vulnerable area; in Saint Louis, the critical zones were located mostly in the northern part of the study area, where both low quality of soil and overexploitation of vegetation, due to grazing and domestic use, increase the sensitivity to desertification. The described methodological approach has a potential to represent a valuable tool to orientate effective policies preventing and mitigating land degradation processes. Model validation and comparison with other widely applied methods to assess desertification are in progress.

Nous developpons une theorie generale pour des equations d’evolution de type hyperbolique parabol... more Nous developpons une theorie generale pour des equations d’evolution de type hyperbolique parabolique non lineaire a l’aide de la theorie des semi-groupes non lineaires dans les espaces de Banach. Nous etablissons des resultats d’existence, d’unicite et de dependance continue par rapport aux donnees d’une bonne solution du probleme de Cauchy ou des problemes aux limites associees a cette equation sous des hypotheses tres generales. Avec des hypotheses complementaires, nous montrons que cette bonne solution est une solution locale de type entropique, nous etudions egalement l’unicite des solutions faibles et l’existence de solution forte.

Dans cette these, nous regroupons quatre articles dans lesquels, nous etudions divers aspects mat... more Dans cette these, nous regroupons quatre articles dans lesquels, nous etudions divers aspects mathematiques de problemes paraboliques fortement degeneres en une dimension d'espace. Dans le premier et le second article nous etudions une equation generale de type parabolique pouvant degeneree en hyperbolique du premier ordre pour certaines valeurs des variables. Dans le premier article, nous developpons une notion de solution entropique du probleme stationnaire associe a cette equation. Ceci nous permet, suivant la theorie des semi-groupe non lineaire dans un espace de banach, d'associer aux donnees un operateur de cet espace de banach. Nous montrons que cet operateur est fortement accretif a domaine dense et verifie la condition d'image. Dans le second article, nous etablissons des resultats d'existence, d'unicite et de dependance continue par rapport aux donnees, d'une bonne solution du probleme de cauchy ou de problemes aux limites associes a cette equation ...

Annales de l'Institut Henri Poincare (C) Non Linear Analysis

Springer proceedings in mathematics & statistics, 2019

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost ... more This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D α t x(t) = Ax(t) + D α-1 t F(t, x(t)), t ∈ R, where 1 < α < 2, A is a linear densely defined operator of sectorial type of ω < 0 on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation.

Afrika Matematika, 2012

ABSTRACT

Comptes rendus de l' …, 1994

... Titre du document / Document title. COMPACT ATTRACTORS FOR REACTION-DIFFUSION EQUATIONS IN RN... more ... Titre du document / Document title. COMPACT ATTRACTORS FOR REACTION-DIFFUSION EQUATIONS IN RN. Auteur(s) / Author(s). FEIREISL E. ; LAURENCOT P. ; SIMONDON F. ; TOURE H. ; Revue / Journal Title. Comptes rendus de l&#x27;Académie des sciences. ...

Afrika Matematika, 2012

In this work, a Schaefer fixed-point theorem is used to investigate the existence of solutions fo... more In this work, a Schaefer fixed-point theorem is used to investigate the existence of solutions for first order impulsive functional differential with variable times.

Cubo (Temuco), 2014

Motivated by the recent works by the first and the second named authors, in this paper we introdu... more Motivated by the recent works by the first and the second named authors, in this paper we introduce the notion of doubly-weighted pseudo-almost periodicity (respectively, doubly-weighted pseudo-almost automorphy) using theoretical measure theory. Basic properties of these new spaces are studied. To illustrate our work, we study, under Acquistapace-Terreni conditions and exponential dichotomy, the existence of (µ, ν)pseudo almost periodic (respectively, (µ, ν)-pseudo almost automorphic) solutions to some nonautonomous partial evolution equations in Banach spaces. A few illustrative examples will be discussed at the end of the paper. RESUMEN Motivado por los trabajos recientes del primer y segundo autor, en este artículo introducimos la noción de seudo-casi periodicidad con doble peso (seudo-casi automorfía con doble peso respectivamente) usando Teoría de la Medida. Se estudian las propiedades básicas de estos espacios nuevos. Para ilustrar nuestro trabajo, bajo las condiciones de Acquistapace-Terreni y dicotomía exponencial estudiamos la existencia de soluciones (respectivamente, (µ, ν) seudo-casi periódicas (µ, ν) seudo-casi automórficas) para algunas ecuaciones parciales de evolución autónomas en espacios de Banach. Algunos ejemplos ilustrativos se discutirán al final del artículo.

We show in this paper the continuous dependence of mild solutions of =a\bigl(u, arphi(u)_x\bigr)_... more We show in this paper the continuous dependence of mild solutions of =a\bigl(u, arphi(u)_x\bigr)_x+v$ on =]0,T[ imes I$ with respect to the open interval $.

Afrika Matematika, 2012

ABSTRACT

Nonlinear Analysis: Theory, Methods & Applications, 2012

This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost ... more This work is concerned with the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a class of semilinear fractional differential equations, D α t x(t) = Ax(t) + D α-1 t F(t, x(t)), t ∈ R, where 1 < α < 2, A is a linear densely defined operator of sectorial type of ω < 0 on a complex Banach space X and F is an appropriate function defined on phase space. The fractional derivative is understood in the Riemann-Liouville sense. The results obtained are utilized to study the existence and uniqueness of weighted Stepanov-like pseudo-almost automorphic mild solutions for a fractional relaxation-oscillation equation.

Nonlinear Analysis: Theory, Methods & Applications, 2009

In this work, we study the existence and regularity of solutions for some partial functional inte... more In this work, we study the existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces. We suppose that the undelayed part admits a resolvent operator in the sense of Grimmer [R. Grimmer, Resolvent operators for integral ...

Nonlinear Analysis: Theory, Methods & Applications, 2009

In this work, we establish several results about the existence and regularity of solutions for so... more In this work, we establish several results about the existence and regularity of solutions for some neutral partial di erential equations with nonlocal conditions. We assume that the linear part generates a strongly continuous semigroup on a general Banach space.

CLUVA (CLimate change and Urban Vulnerability in Africa; http://www.cluva.eu/) is a 3 years proje... more CLUVA (CLimate change and Urban Vulnerability in Africa; http://www.cluva.eu/) is a 3 years project, funded by the European Commission in 2010. Its main objective is the estimate of the impacts of climate changes in the next 40 years at urban scale in Africa. The mission of CLUVA is to develop methods and knowledge to assess risks cascading from climate-changes. It downscales IPCC climate projections to evaluate threats to selected African test cities; mainly floods, sea-level rise, droughts, heat waves and desertification. The project evaluates and links: social vulnerability; vulnerability of in-town ecosystems and urban-rural interfaces; vulnerability of urban built environment and lifelines; and related institutional and governance dimensions of adaptation. A multi-scale and multi-disciplinary quantitative, probabilistic, modelling is applied. CLUVA brings together climate experts, risk management experts, urban planners and social scientists with their African counterparts in a...

ABSTRACT The United Nations Convention to Combat Desertification (UNCCD) defines desertification ... more ABSTRACT The United Nations Convention to Combat Desertification (UNCCD) defines desertification as &quot;land degradation in arid, semi-arid and dry sub-humid areas resulting from various factors, including climatic variations and human activities&quot;. Desertification is regarded as one of the major global environmental problems of the 21st century and the African sub-Sahara is often quoted as the most seriously affected region with a significant loss of biological and economic productivity of the land. In this geographic area, desertification processes are usually generated by soil erosion due to climate characteristics and fluctuations, unsustainable land uses, overgrazing and inappropriate agricultural practices. Preventing desertification requires an improved understanding of its causes, impact, degree and association with climate, soil, water, land cover, socio-economic factors and their combined effects. The development of methodologies capable of managing large amounts of data in an integrated approach is needed because of the complexity and variety of forms of desertification processes. The study was carried out within the FP7-ENV-2010 CLUVA project (CLimate change and Urban Vulnerability in Africa), aimed to estimate the sensitivity to land degradation in the urban and peri-urban areas of both Ouagadougou (Burkina Faso) and Saint Louis (Senegal) cities. The approach was based on the implementation and adaptation of the modeling methodology developed within the MEDALUS project (MEditerranean Desertification and Land Use). The model is characterized by a multi-factor approach based on the assessment of both environmental quality indicators (climate, soil, vegetation) and anthropogenic factors (land management). The methodology is adaptable to the local conditions, considering that some key indicators can be operationally defined through the inclusion or exclusion of parameters and the scores assigned in order to match the specific relevance of the factors. All local data, arranged in a GIS environment, allowed the generation of maps identifying Environmentally Sensitive Areas (ESAs) and Indices of Environmental Sensitivity (ESAI). As expected, the results highlighted an overall high sensitivity to desertification. In Ouagadougou, the poorly vegetated peri-urban zone, affected by an increasing demographic pressure as the result of immigration from surrounding rural areas, was found as the most vulnerable area; in Saint Louis, the critical zones were located mostly in the northern part of the study area, where both low quality of soil and overexploitation of vegetation, due to grazing and domestic use, increase the sensitivity to desertification. The described methodological approach has a potential to represent a valuable tool to orientate effective policies preventing and mitigating land degradation processes. Model validation and comparison with other widely applied methods to assess desertification are in progress.

Nous developpons une theorie generale pour des equations d’evolution de type hyperbolique parabol... more Nous developpons une theorie generale pour des equations d’evolution de type hyperbolique parabolique non lineaire a l’aide de la theorie des semi-groupes non lineaires dans les espaces de Banach. Nous etablissons des resultats d’existence, d’unicite et de dependance continue par rapport aux donnees d’une bonne solution du probleme de Cauchy ou des problemes aux limites associees a cette equation sous des hypotheses tres generales. Avec des hypotheses complementaires, nous montrons que cette bonne solution est une solution locale de type entropique, nous etudions egalement l’unicite des solutions faibles et l’existence de solution forte.

Dans cette these, nous regroupons quatre articles dans lesquels, nous etudions divers aspects mat... more Dans cette these, nous regroupons quatre articles dans lesquels, nous etudions divers aspects mathematiques de problemes paraboliques fortement degeneres en une dimension d'espace. Dans le premier et le second article nous etudions une equation generale de type parabolique pouvant degeneree en hyperbolique du premier ordre pour certaines valeurs des variables. Dans le premier article, nous developpons une notion de solution entropique du probleme stationnaire associe a cette equation. Ceci nous permet, suivant la theorie des semi-groupe non lineaire dans un espace de banach, d'associer aux donnees un operateur de cet espace de banach. Nous montrons que cet operateur est fortement accretif a domaine dense et verifie la condition d'image. Dans le second article, nous etablissons des resultats d'existence, d'unicite et de dependance continue par rapport aux donnees, d'une bonne solution du probleme de cauchy ou de problemes aux limites associes a cette equation ...

Annales de l'Institut Henri Poincare (C) Non Linear Analysis