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
What's
new?
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,
Discrete Contin. Dyn. Syst. Ser. S. 17 (2024), 1460--1484.
- 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, Analyse de dynamiques d'échanges
microscopiques et macroscopiques pour l'écologie et
l'épidémiologie, PhD defended Sept. 2024.
- 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.