Publications

A. Ducrot and Z. Jin, Spreading speeds for nonautonomous Fisher-KPP equation with nonlocal diffusion, Journal of Nonlinear Sciences, 2023, 33, 100.
L.Deng and A. Ducrot, Pulsating waves in a multidimensional reaction-diffusion system of epidemic type, J. European Math. Soc., to appear.
A. Ducrot, H. Kang and S. Ruan, Age-structured Models with Nonlocal Diffusion of Dirichlet Type, I: Principal spectral theory and limiting properties, Journal d'Analyse Mathématique, to appear.
A. Ducrot, H. Kang and S. Ruan, Age-structured Models with Nonlocal Diffusion of Dirichlet Type, II: Global Dynamics, Israel Journal of Mathematics, to appear.
J.B. Burie, A. Ducrot and Q. Griette, Asymptotic behavior of an epidemic model with infinitely many variants, Journal of Mathematical Biology, to appear.
A. Moussaoui, A. Ducrot, A. Moulai-Khatir and P. Auger, A model of a fishery with fish storage and variable price involving delay equations, Math. Biosci., 2023, 109022.
A. Ducrot and Z. Jin, Speading speeds for time heterogeneous reaction-diffusion systems of the prey-predator type , Nonlinear Analysis RWA, 2023, 74, 103923.
L. Deng and A. Ducrot, Existence of multi-dimensional pulsating fronts for KPP equations: a new formulation approach, Calculus of Variations and Partial Differential Equations, 2023, 62, 134.
M. Alfaro, A. Ducrot and H. Kang, Quantifying the threshold phenomena for propagation in nonlocal diffusion equations, SIAM Journal on Mathematical Analysis, 2023, 55, 1596-1630.
A. Ducrot, H. Kang and P. Magal, A short proof for Hopf bifurcation in Gurtin-MacCamy's population dynamics model, Proc. Amer. Math. Soc., 2023, 151, 3561-3575
A. Ducrot, D. Manceau and A. Sylla, Spreading speed for an spidemic system modelling plant disease with adaptation, DCDS B, 2023, 28, 2011-2043.
I. Ahn, W. Choi, A. Ducrot and J.-S. Guo, Spreading Dynamics for a three Species Predator-Prey System with two preys in a shifting environment, Journal of Dynamics and Differential Equations, 2022, 1-29.
A. Ducrot, H. Kang and P. Magal, Hopf bifurcation theorem for second order semi-linear Gurtin-MacCamy equation, Journal of Evolution Equations, 2022, 22, pp 72.
A. Ducrot and P. Magal, Return-to-home model for short-range human travel, Mathematical Biosciences and Engineering MBE, 2022, 19, 7737-7755.
A. Ducrot and Z. Jin, Generalized travelling fronts for non-autonomous Fisher-KPP equations with nonlocal diffusion, Annali di Matematica Pura ed Applicata, 2021, 1-32.
G. Cantin, A. Ducrot, B.M. Funatsu, Mathematical modeling of forest ecosystems by a reaction-diffusion-advection system: impacts of climate change and deforestation, Journal of Mathematical Biology, 8 (2021), 1-45.
A. Ducrot, P. Magal and A. Thorel, An integrated semigroup approach for age structured equations with diffusion and non-homogeneous boundary conditions, Nonlinear Differential Equations and Applications NoDEA, 2021, 28, 49.
F. Fabre, J.-B. Burie, A. Ducrot, S. Lion, Q. Richard, R. Djidjou-Demasse, An epi-evolutionary model for predicting the adaptation of spore-producing pathogens to quantitative resistance in heterogeneous environments, Evolutionary Applications, 2021.
L. Abi Rizk, J.-B. Burie and A. Ducrot, Asymptotic speed of spread for a nonlocal evolutionary-epidemic system, DCDS A, 41 (2021), 4959-4985.
A. Ducrot, T. Giletti, J.-S. Guo and M. Shimojo, Asymptotic spreading speeds for a predator-prey system with two predators and one prey, Nonlinearity, 34 (2021), 669-704.
A. Ducrot, Spreading speed for a KPP type reaction-diffusion system with heat losses and fast decaying initial data, Journal of Differential Equations, 270 (2021), 217–247.
A. Ducrot, Z. Liu and P. Magal, Large Speed Traveling Waves for the Rosenzweig- MacArthur predator-prey Model with Spatial Diffusion, Physica D, 415 (2021), 132730.
J.-B. Burie, A. Ducrot, Q. Griette and Q. Richard, Concentration estimates in a multi- host epidemiological model structured by phenotypic traits, Journal of Differential Equations, 269 (2020), 11492–11539.
B. Ambrosio, A. Ducrot and S. Ruan, Generalized traveling waves for time-dependent reaction–diffusion systems, Mathematische Annalen, 381 (2021), 1-27. PDF
A. Ducrot and D. Manceau, A one-dimensional logistic like equation with nonlinear and nonlocal diffusion: strong convergence to equilibrium, Proc. Amer. Math. Soc., 148 (2020), 3381-3392. PDF
M. Alfaro, A. Ducrot and G. Faye, Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations, SIAM J. Appl. Dyn. Syst., 19 (2020), 1291-1311. PDF
A. Ducrot and A. Genadot, Self-Similar Behavior of a Nonlocal Diffusion Equation with Time Delay, SIAM J. Math. Anal. 52 (2020), 2275-2312. PDF
A. Ducrot, T. Giletti and H. Matano, Spreading speeds for multidimensional reaction-diffusion systems of the prey-predator type, Calculus of Variations and Partial Differential Equations, 58, 137 (2019). PDF
J.-B. Burie, R. Djidjou-Demasse and A. Ducrot, Slow convergence to equilibrium for an evolutionary epidemiology integro-differential system, Discrete & Continuous Dynamical Systems - B, 2019, 22, PDF
A. Ducrot, P. Magal, T. Nguyen and G Webb, Identifying the number of unreported cases in SIR epidemic models, Mathematical Medicine and Biology, Oxford University Press (OUP), 2019.
L. Abi Rizk, J.-B. Burie and Arnaud Ducrot, Travelling wave solutions for a non-local evolutionary-epidemic system Journal of Differential Equations, 267 (2019), 1467-1509.
E. Augeraud-Véron and A. Ducrot, Spatial externality and indeterminacy, Mathematical Modelling of Natural Phenomena, (2019)14 , pp. 102.
A. Ducrot, J.-S. Guo, G. Lin and S. Pan, The spreading speed and the minimal wave speed of a predator–prey system with nonlocal dispersal, Zeitschrift für Angewandte Mathematik und Physik, (2019) 70.
A. Ducrot and P. Magal, A center manifold for second order semi-linear differential equations on the real line and applications to the existence of wave trains for the Gurtin-McCamy equation, Trans. Amer. Math. Soc., 372 (2019), 3487-3537. . PDF
A. Ducrot and P. Magal, Integrated Semigroups and Parabolic Equations. Part II: Semilinear Problems, Annali della Scuola Normale Superiore Di Pisa, Classe di Scienze, XX (2020), 1071-1111. PDF
J.-B. Burie, R.D. Demasse and A. Ducrot, Asymptotic and transient behaviour for a nonlocal problem arising in population genetics, European Journal of Applied Mathematics, to appear. PDF
A. Ducrot, X. Fu and P. Magal, Turing Hopf bifurcation for a reaction diffusion equation with nonlocal advection, Journal of Nonlinear Sciences, 18 (2018), 1959-1997.PDF
M. Alfaro and A. Ducrot, Population invasion with bistable dynamics and adaptive evolution: the evolutionary rescue, Proc. Amer. Math. Soc., 146 (2018), 4787-4799. PDF
A. Ducrot and J.-S. Guo, Asymptotic behaviour of solutions to a class of diffusive predator-prey systems, Journal of Evolution Equations, 18 (2018), 755-775.
A. Ducrot, J.-S. Guo and M. Shimojo, Behaviors of solutions for a singular prey-predator model and its shadow system, Journal of Dynamics and Differential Equations, 30 (2018), 1063-1079.
M. Alfaro, A. Ducrot and T. Giletti, Travelling waves for a non-monotone bistable equation with delay: existence and oscillations, Proceedings of the London Mathematical Society, 116 (2018), 729-759. PDF
J.-B. Burie, A. Ducrot and A.A. Mbengue, Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants, Discrete Contin. Dyn. Syst. Ser. B 22 (2017), 2879–2905.
R. Djidjou-Demasse, A. Ducrot and F. Fabre, Steady state concentration for a phenotypic structured problem modelling the evolutionary epidemiology of spore producing pathogens, Mathematical Models and Methods in Applied Sciences, 27 (2017), 385–426. PDF
A. Ducrot, P. Magal and O. Seydi, Singular perturbation for an abstract non-densely defined Cauchy problem, Journal of Evolution Equations, 17 (2017), 1089–1128. PDF
A. Ducrot, Spatial propagation for a two component reaction-diffusion system arising in population dynamics, Journal of Differential Equations, 260 (2016), 8316–8357. PDF
A. Ducrot, P. Magal and O. Seydi, A singularly perturbed Delay Differential Equation modeling nosocomial infections, Differential and Integral Equations, 29 (2016), 321-358. PDF
A. Ducrot and H. Matano, Plant disease propagation in a striped periodic medium. Applied analysis in biological and physical sciences, 121–164, Springer Proc. Math. Stat., 186, Springer, New Delhi, 2016.
A. Ducrot, A multi-dimensional bistable nonlinear diffusion equation in a periodic medium, Mathematische Annalen, 366 (2016), 783–818. PDF
A. Ducrot, P. Magal and O. Seydi, Persistence of exponential trichotomy for linear operators: A Lyapunov-Perron approach , Journal of Dynamics and Differential Equations, 28 (2016), 93–126. PDF
A. Ducrot, On the large time behaviour of the multi-dimensional Fisher-KPP equation with compactly supported initial data, Nonlinearity, 28 (2015), 1043--1076. PDF
C. Benosman, B. Ainseba and A. Ducrot, Optimization of Cytostatic Leukemia Therapy in an Advection–Reaction–Diffusion Model, Journal of Optimization Theory and Applications, 167 (2015), 296--325.
J.B. Burie and A. Ducrot, A field scale model for the spread of fungal diseases in crops: the example of a powdery mildew epidemic over a large vineyard, Mathematical Methods in the Applied Sciences, 38 (2015), 3720-3737.
A. Ducrot, P. Magal and O. Seydi, A finite-time condition for exponential trichotomy in infinite dynamical systems, Canadian Journal Math., 38 (2015), 3720-3737.
P. Zongo, A. Ducrot, J.-B. Burie and C. Beaumont, Prevalence of Salmonella in flocks housed in enriched cages, Epidemiology and Infection, 38 (2015), 3720--3737.
A. Ducrot and P. Magal, Asymptotic behaviour of a non-local diffusive logistic equation , SIAM Journal on Mathematical Analysis, 46 (2014), 1731-1753. PDF
A. Ducrot and G. Nadin, Asymptotic behaviour of travelling waves for the delayed Fisher-KPP equation , Journal of Differential Equations, 256 (2014), 3115-3140. PDF
A. Ducrot and T. Giletti, Convergence to a pulsating travelling wave for an epidemic reaction-diffusion system with non-diffusive susceptible population, Journal of Mathematical Biology, 69 (2014), 533-552. PDF
M. Alfaro and A. Ducrot, Propagating interface in a monostable reaction-diffusion equation with time delay , Differential and Integral Equations, 27 (2014), 81-104. PDF
A. Ducrot and M. Langlais, Global weak solution for a singular two component reaction-diffusion system, Bulletin of the London Mathematical Society, 46 (2014), 1--13. PDF
A. Ducrot, T. Giletti and H. Matano, Existence and convergence to a propagating terrace in one-dimensional reaction-diffusion equations, Trans. A.M.S., 366 (2014), 5541--5566. PDF
R.D. Demasse and A. Ducrot, An age-structured within-host model for multi-strain malaria infections, SIAM Journal on Applied Mathematics, 73 (2013), 572--593. PDF
A. Ducrot, Convergence to generalized transition waves for some Holling-Tanner prey- predator reaction-diffusion system, Journal de Mathématiques Pures et Appliquées, 100 (2013), 1--15. PDF
A. Ducrot and S. Madec, Singularly perturbed elliptic system modelling the competitive interactions for a single resource, Mathematical Models and Methods in Applied Sciences, 23 (2013), 1939-1977. PDF
C. Beaumont, J.B. Burie, A. Ducrot and P. Zongo, Propagation of Salmonella within an industrial hens house, SIAM Journal on Applied Mathematics, 72 (2012), 1113--1148. PDF
A. Ducrot, M. Langlais and P. Magal, Multiple travelling waves for an SI-epidemic models, Networks and Heterogeneous Media, 8 (2013), 171--190.
A. Ducrot and J.-S. Guo, Quenching behaviour for a singular predator-prey model, Nonlinearity 25 (2012), 2059--2073. PDF
A. Ducrot and M. Langlais, A singular reaction-diffusion system modelling predator-prey interactions: invasion and co-extinction waves, Journal of Differential Equations 253 (2012), 502--532. PDF
H. d’Albis, E. Augeraud-Véron, E. Djemai and A. Ducrot, The Dispersion of Age Difeferences between Partners and the Asymptotic Dynamics of the HIV Epidemic, Journal of Biological Dynamics, 6 (2012), 695--717.
A. Ducrot, P. Magal and S. Ruan, Projectors on the generalized eigenspaces for partial differential equations with delay, in ``Infinite Dimensional Dynamical Systems'', J. Mallet-Paret, J. Wu, Y. Yi, and H. Zhu (eds.), Fields Institute Communications Vol. 64, 353-390. PDF
A. Ducrot, M. Langlais and P. Magal, Qualitative analysis and travelling wave solutions for the SI model with vertical transmission, Communication in Pure and Applied Analysis, 11 (2012), 97--113. PDF
A. Ducrot and P. Magal, Travelling wave solution for infection-age structured model with vital dynamics, Nonlinearity 24 (2011), 2891--2911. PDF
J. Arino, A. Ducrot and P. Zongo, A metapopulation model for malaria with transmission-blocking partial immunity in hosts, Journal of Mathematical Biology 64 (2012), 423--448. PDF
M. Alfaro and A. Ducrot, Sharp Interface limit of the Fisher-KPP equation, Communication in Pure and Applied Analysis 11 (2012), 1--18. PDF
A. Ducrot, F. Le Foll, P. Magal, H. Murakawa, J. Pasquier and G. F. Webb, An in vitro cell population dynamics model incorporating cell size, quiescence, and contact inhibition, Mathematical Models and Methods in Applied Sciences 21 (2011), Suppl. 871--892. PDF
A. Ducrot, P. Magal and O. Seydi, Nonlinear boundary conditions derived by singular perturbation in age structured population dynamics model, Journal of Applied Analysis and Computation, 1 (2011), 373--395. PDF
M. Alfaro and A. Ducrot, Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay, DCDS B, 16 (2011), 15--29. PDF
A. Ducrot, M. Marion and V. Volpert, Spectrum of some integro-differential operators and stability of travelling waves, Nonlinear Analysis T.M.A., 74 (2011), 4455--4473. PDF
A. Ducrot, Travelling waves for a size and space structured model in population dynamics: Point to sustained oscillating solution connections, Journal of Differential Equations, 250 (2011), 410--449. PDF
A. Ducrot, V. Guyonne and M. Langlais, Some remarks on the qualitative properties of solutions to a predator-prey model posed on non coincident spatial domains, DCDS S, 4 (2011), 67--82.
I. Demin, A. Ducrot and V. Volpert, Spatial distribution of cell populations in the process of erythropoiesis, IEJPAM, 01 (2010), 143--161. PDF
A. Ducrot, P. Magal and S. Ruan, Une introduction aux modèles de dynamique de populations structurées en âges et aux problèmes de bifurcations, Gazette des mathématiciens, 125 (2010), 27--40. PDF
A. Ducrot, P. Magal and S. Ruan, Travelling wave solutions in multi-group age-structured epidemic models , Arch. Rational Mech. Anal., 195 (2010), 311--331. PDF
A. Ducrot, Z. Liu and P. Magal, Projectors on the generalized eigenspaces for neutral functional differential equations in Lp spaces, Canadian Journal of Mathematics, 62 (2010), 74--93. PDF
A. Ducrot, K. Prevost and P. Magal, Integrated semigroup and parabolic equation: Part I, linear perturbation of almost sectorial operators, Journal of Evolution Equations, 10 (2010), 263--291. PDF
A. Bonneu, T. Fourcaud, A. Ducrot and M. Langlais, Proposition of a conceptual density based model to describe fine root networks in tree root systems. Proc. of the Third International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications, Li, B., Guo, Y., Jaeger, M. (Eds). Los Alamitos : IEEE Computer Society (2010), pp. 18--25.
J.B. Burie and A. Ducrot, Travelling waves solution for some models in phytopathology, Nonlinear Analysis RWA 10 (2009), pp. 2307-2325.
A. Ducrot and P. Magal, Travelling wave solutions for an infection-age stuctured model with diffusion, Proc. Roy. Soc. Edimburg. A 139 (2009), 459--482. PDF
N. Apreutesei, A. Ducrot and V. Volpert, Travelling Waves for Integro-differential Equations, DCDS B, 11 (2009), 541--561.
M. Adimy, A. Ducrot and C. Kou, On the dynamics of an impulsive model of hematopoiesis, Math. Mod. Natural Phenomena, 4 (2009), 68--91. PDF
A. Ducrot, S.B. Sirima, B. Somé and P. Zongo, A mathematical model for malaria involving differential susceptibility, exposedness and infectivity of human host, Journal of Biological Dynamics, 3 (2009), 574--598. PDF
J. Chu, A. Ducrot, P. Magal and S. Ruan, Hopf bifurcation for a size structured population dynamics model with random growth, Journal of Differential Equations, 247 (2009), 956--1000. PDF
P. Auger and A. Ducrot, A model of fishery with fish stock involving delay equations, Phi. Trans. Roy. Soc. A 367 (2009), 4907--4922.
A. Ducrot, Z. Liu and P. Magal, Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems, J. Math. Anal. Appl. 341, pp. 501-518 (2008).
A. Ducrot and M. Langlais, Travelling waves in invasion processes with pathogens, Mathematical Models and Methods in Applied Sciences, 18 (2008), 325--349.
A. Ducrot, M. Marion and V. Volpert, Reaction-diffusion problems with non Fredholm operators, Adv. Diff. Equations, 13 (2008), 1151-1192.
N. Apreutesei, A. Ducrot and V. Volpert, Competition of species with intra-specific competition, Math. Modelling of Natural Phenomena, 3 (2008), 1-27.
A. Ducrot, M. Marion, V. Volpert. Reaction-diffusion waves (with the Lewis number different from 1). Publibook, Paris (2008).
A. Ducrot, Travelling wave solutions for a scalar age-structured equation, DCDS B, 7 (2007), 251--273.
A. Ducrot and V. Volpert, On a model of leukemia development with a spatial cell distribution, Math. Modelling of Natural Phenomena, 2 (2007), 101--120.
K. Allali, A. Ducrot, A. Taik and V. Volpert, Convective instability of reaction fronts in porous media, Math. Modelling of Natural Phenomena, 2 (2007), 20--39.
A. Ducrot, Structural Stability of Combustion Models with complex chemistry, Mathematical Models and Methods in Applied Sciences, 16 (2006), 793--817.
A. Ducrot, M. Marion and V. Volpert, Reaction-diffusion-convection systems with non Fredholm operators, Int. J. Pure Appl. Math, 27 (2006), 179--204.
A. Ducrot, Multi-dimensional combustion waves for Lewis number close to one, Mathematical Methods in the Applied Sciences, 30 (2006), 291--304.
J.B. Burie, A. Calonnec and A. Ducrot, Singular perturbation analysis of travelling waves for a model in phytopathology, Math. Modelling of Natural Phenomena, 01 (2006), 49--63.
N. Bessonov, A. Ducrot and V. Volpert, Modelling of Leukemia development in the bone marrow, Proc. of the annual Symposium on "Mathematics applied in Biology and Biophysics", Tome XLVIII, vol.2 (2005), 79--88.
S. Bidali, A. Ducrot, A. Mariani and M. Rustici, Self-ignition of Polymerization fronts with convection : the "Rainstorm Effect", e-Polymers, 44 (2005).
A. Ducrot and V. Volpert, Modelling of convective heat explosion, Journal of Technical Physics, 46 (2005), 129--143.
A. Ducrot, M. Marion and V. Volpert, Systèmes de Réaction-Diffusion sans Propriété de Fredholm, CRAS, 340 (2005), 659--664.
A. Ducrot and M. Marion, Two-dimensional travelling wave solutions of a system modeling near-equi-diffusional flames, Nonlinear Analysis, TMA, 61 (2005), 1105--1134. PDF