Matthieu Alfaro 

      
Professor of applied maths at the Laboratoire of Mathématiques Raphaël Salem (LMRS),                                                                                                           
UMR CNRS 6085, Université de Rouen Normandie, France.  
Email address: firstname.familyname@univ-rouen.fr

• GT biomaths normand.
• M. A. and P. Jouan, The Allen-Cahn equation with nonlinear truncated Laplacians: description of radial solutions.
• M. A. and C. Chainais-Hillairet, Long time behavior of the field-road diffusion model: an entropy method and a finite volume scheme.
• M. A., G. Raoul and O. Ronce, When do leading and rear edges of the range shift slower or faster than climate? Insights from a mathematical model.
• Q. Griette, M. A., G. Raoul and S. Gandon, Evolution and spread of multi-adapted pathogens in a spatially heterogeneous environment (main text) and supplementary information. to appear in Evolution Letters.
  

Research interests in PDEs:

• Reaction-diffusion equations: Interface dynamics, Traveling waves in nonlocal population dynamics' models, Heterogeneity, Evolutionary biology, Epidemiology, Blow-up phenomena...
• Elliptic equations: Nonlinear degenerate operators, Liouville type results...
  
• Fractal conservation laws: Entropy solutions, Regularizing effect of the fractional Laplacian...

Publications and preprints:

• M. A., F. Hamel and L. Roques, Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation, to appear in Discrete Contin. Dyn. Syst. Ser. S. 
• M. A., F. Hamel, F. Patout and L. Roques, Adaptation in a heterogeneous environment. Part II: To be three or not to be, J. Math. Biol. 87 (2023), Paper No. 68.
• M. A., R. Ducasse and S. Tréton, The field-road diffusion model: fundamental solution and asymptotic behavior, J. Differential Equations 367 (2023), 332--365.
• M. A. and D. Xiao, Lotka-Volterra competition-diffusion system: the critical competition case, Comm. Partial Differential Equations 48 (2023), 182--208. 
• M. A., A. Ducrot and H. Kang, Quantifying the threshold phenomena for propagation in nonlocal diffusion equations, SIAM J. Math. Anal. 55 (2023), 1596--1630.
  
• M. A., P. Gabriel and O. Kavian, Confining integro-differential equations originating from evolutionary biology: ground states and long time dynamics, Discrete Contin. Dyn. Syst. Ser. B. 28 (2023), 5905--5933.
• M. A., T. Giletti, Y.-J. Kim, G. Peltier and H. Seo, On the modeling of spatially heterogeneous nonlocal diffusion: deciding factors and preferential position of individuals, J. Math. Biol. 84 (2022), Paper No. 38.
• M. A., Q. Griette, D. Roze and B. Sarels, The spatio-temporal dynamics of interacting incompatibilities. Part I: The case of stacked underdominant clines, J. Math. Biol. 84 (2022), Paper No. 20.
• M. A. and G. Peltier, Populations facing a nonlinear environmental gradient: steady states and pulsating fronts, Math. Models Methods Appl. Sci. 32 (2022), 209--290.
• F. Patout, R. Forien, M. A., J. Papaïx and L. Roques, The emergence of a birth dependent mutation rate: causes and consequences, PCI Math Comp Biol. (2021).
• M. A., L. Girardin, F. Hamel and L. Roques, When the Allee threshold is an evolutionary trait: persistence vs. extinction, J. Math. Pures Appl. 155 (2021), 155--191.
• M. A. and O. Kavian, Blow-up phenomena for positive solutions of semilinear diffusion equations in a half-space: the influence of the diffusion kernel, Ann. Fac. Sci. Toulouse Math. 31 (2022), 1259--1286.
• M. A., 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.
  
• M. A. and I. Birindelli, Evolution equations involving nonlinear truncated Laplacian operators, Discrete Contin. Dyn. Syst. A 40 (2020), 3057--3073.
• M. A. and M. Veruete, Density dependent replicator-mutator models in directed evolution, Discrete Contin. Dyn. Syst. Ser. B 25 (2020), 2203--2221.
• M. A. and T. Giletti, Interplay of nonlinear diffusion, initial tails and Allee effect on the speed of invasions,  Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 21 (2020), 1223--1255.
• M. A., D. Antonopoulou, G. Karali and H. Matano, Generation of fine transition layers and their dynamics for the stochastic Allen-Cahn equation, preprint.
• M. A and T. Giletti, When fast diffusion and reactive growth both induce accelerating invasions, Commun. Pure Appl. Anal. 18 (2019), 3011--3034.
• M. A. and M. Veruete, Evolutionary branching via replicator-mutator equations, J. Dynamics Differential Equations 31 (2019), 2029--2052.
• M. A. and A. Ducrot, Population invasion with bistable dynamics and adaptive evolution: the evolutionary rescue, Proc. Amer. Math. Soc. 146 (2018), 4787--4799.
• M. A., H. Izuhara and M. Mimura, On a nonlocal system for vegetation in drylands, J. Math. Biol. 77 (2018), 1761--1793.
• M. A. and R. Carles, Superexponential growth or decay in the heat equation with a logarithmic nonlinearity, Dyn. Partial Differ. Equ. 14 (2017), 343--358.
• M. A., A. Ducrot and T. Giletti, Travelling waves for a non-monotone bistable equation with delay: existence and oscillations, Proc. London Math. Soc. 116 (2018),  729--759.
• M. A. and R. Carles, Replicator-mutator equations with quadratic fitness, Proc. Amer. Math. Soc. 145 (2017), 5315--5327. 
• M. A. and J. Coville, Propagation phenomena in monostable integro-differential equations:  acceleration or not?, J. Differential Equations 263 (2017), 5727--5758. 
• M. A. and Q. Griette, Pulsating fronts for  Fisher-KPP systems with mutations as  models in evolutionary epidemiology, Nonlinear Anal. Real World Appl.  42 (2018), 255--289.
• M. A., Fujita blow up phenomena and hair trigger effect: the role of dispersal tails, Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), 1309--1327.
• M. A., H. Berestycki and G. Raoul, The effect of climate shift on a species submitted to dispersion, evolution, growth and nonlocal competition, SIAM J. Math. Anal.  49 (2017), 562--596.
• M. A., Slowing Allee effect vs. accelerating heavy tails in monostable reaction diffusion equations, Nonlinearity 30 (2017), 687--702.
  
• M. A. and T. Giletti, Asymptotic analysis of a monostable equation in periodic media, Tamkang J. Math. (special issue) 47 (2016), 1--26.
• M. A. and T. Giletti, Varying the direction of propagation in reaction-diffusion equations in periodic media, Netw. Heterog. Media 11 (2016), 369--393.
• M. A. and R. Carles, Explicit solutions for replicator-mutator equations: extinction vs. acceleration, SIAM J. Appl. Math. 74 (2014), 1919--1934.  
• M. A. and P. Alifrangis, Convergence of a mass conserving Allen-Cahn equation whose Lagrange multiplier is nonlocal and local, Interfaces Free Bound. 16 (2014), 243--268. 
• M. A., J. Coville and G. Raoul, Bistable travelling waves for nonlocal reaction diffusion equations, Discrete Contin.  Dyn.  Syst.  Ser.  A. 34 (2014), 1775--1791.
• M. A. and A. Ducrot, Propagating interface in a monostable reaction-diffusion equation with time delay, Differential Integral Equations 27 (2014), 81--104.
• M. A., J. Coville and G. Raoul, Travelling waves in a nonlocal reaction-diffusion equation as a model for a population structured by a space variable and a phenotypic trait, Comm. Partial Differential Equations 38 (2013), 2126--2154.  
• M. A. and J. Coville, Rapid traveling waves in the nonlocal Fisher equation connect two unstable states, Appl. Math. Lett. 25 (2012), 2095--2099.
• M. A. and J. Droniou, General fractal conservation laws arising from a model of detonations in gases,  Appl. Math. Res. Express. 2 (2012), 127--151.
• M. A. and H. Matano, On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data, Discrete Contin. Dyn. Syst. Ser. B. 17 (2012), 1639--1649.
• M. A., J. Droniou and H. Matano, Convergence rate of the Allen-Cahn equation to generalized motion by mean curvature,  J. Evol. Equ. 12 (2012), 267--294.
• M. A. and D. Hilhorst, Interface dynamics of the porous medium equation with a bistable reaction term, Asymptot. Anal. 76 (2012), 35--48.
• M. A. and E. Logak, Convergence to a propagating front in a degenerate Fisher-KPP equation with advection, J. Math. Anal. Appl. 387 (2012), 251--266.
• M. A. and A. Ducrot, Sharp interface limit of the Fisher-KPP equation, Comm. Pure Appl.Anal. 11 (2012), 1--18.
• M. A. and A. Ducrot, Sharp interface limit of the Fisher-KPP equation when initial data have slow exponential decay, Discrete Contin. Dyn. Syst. Ser. B. 16 (2011), 15--29.
• M. A., H. Garcke, D. Hilhorst, H. Matano and R. Schatzle, Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen-Cahn equation,  Proc. Roy. Soc. Edinburgh Sect. A. 140 (2010), 673--706.
• M. A. and D. Hilhorst, Generation of interface for an Allen-Cahn equation with nonlinear diffusion, Math. Model. Nat. Phenom. 5 (2010), 1--12.
• M. A., Generation, motion and thickness of transition layers for a nonlocal Allen-Cahn equation, Nonlinear Anal. 72 (2010), 3324--3336.
• M. A., D. Hilhorst and H. Matano, The singular limit of the Allen-Cahn equation and the FitzHugh-Nagumo system, J. Differential Equations 245 (2008), 505--565.
• M. A., The singular limit of a chemotaxis-growth system with general initial data, Adv. Differential Equations 11 (2006),  1227--1260.

PhD students:

• Nessim Dhaouadi, ongoing PhD Sept. 2022- (with A. Blouza).
• Samuel Tréton, ongoing PhD 2021-.
  
• Gwenaël Peltier, Mathematical analysis of nonlocal models in evolutionary ecology, (with O. Ronce), PhD defended June 2021.
  
• Claire Godineau, Influence de l'homogamie sur l'adaptation des plantes au changement climatique, (with O. Ronce and C. Devaux), PhD defended Nov. 2021.
  
• Mario Veruete, Mathematical analysis of nonlocal models in population dynamics, PhD defended June 2019.
• Quentin Griette, Mathematical models for evolutionary epidemiology, (with S. Gandon and G. Raoul), PhD defended June 2017.
• Pierre Alifrangis, Interfaces, in classical or generalized sense, as singular limit of reaction-diffusion equations, with or without comparison principle, PhD defended Sept. 2013.

Supervised Post-Doc:

• Florian Lavigne, (with L. Roques), Post-Doc 2022-2023 (21 months).
• Dongyuan Xiao, Modélisation mathématique de la diffusion de l'agriculture au Néolithique (MOMAGRI), (with M. Raymond), Post-Doc 2020-2021 (18 months).
• Florian Patout, INRAE Avignon, (with L. Roques), Post-Doc 2019-2021 (24 months).
• Alvaro Mateos Gonzalez, Asexual adpatation under mutation selection and drift: stochastic and deterministic dynamics, (with G. Martin and B. Cloez), Post-Doc 2017-2019 (18 months).

Some projects, miscellaneous:

• Conference RMR 2023: Mathematical Models in Biology and Medecine, June 28-30, Rouen.  
• Projet émergent Région Normandie, 2022-2024.
• MAThematical models for fast diffusion CHAnnels in population dynamics and epidemiology (MATCHA). Project RIN.
• Integro-Differential Equations from EVolutionary biology (DEEV). Member of Project ANR JCJC (Head: S. Mirrahimi), 2020-2024.
  
• Mathématiques pour Individus affrontant des CHangements d'Environnements Latents (MICHEL). Head of project of I-site MUSE, 2018-2021.
  
• Propagation of fronts in cooperative microbial populations. Indo-french project IFCAM with G. Raoul and S. Roy, 2015-2017.
  
• Interfaces Dynamics in Evolution Equations (IDEE). Head of project,  ANR JCJC 2011-2014, with P. Alifrangis, J. Droniou, A. Ducrot, N. Forcadel and C. Imbert.
• Member of GDRI ReaDiNet (Reaction-Diffusion Network in Mathematics and Biomedicine).
  

Teaching (old and present):

• L1: Algèbre linéaire et analyse 1, controle 1, controle 2, controle 3.
• L1: Calculus, controle 1, controle 2.
• L3 biologie: Dynamique des populations, Poly cours TD, controle 1 2015, controle 2 2015, controle 1 2016, controle 2 2016.
• L3/M1: Calcul différentiel et équations différentielles.
• M1: Fourier, Chaleur, Replicator-Mutator. 
• M2: Invasion spatiale en dynamique des populations.
• M2: EDP, exam 2014, exam 2015, exam 2020.
• Leçons analyse prépa agreg2.
• 2023/2024 L3 méca: Poly Traitement du signal, cc1, cc2
  
• 2023/2024 M1: Poly EDO, cc1, correction cc1, cc2, correction cc2
• 2023/2024 L3: Poly Calcul Diff, cc1, cc2.