Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

Positivity preserving and unconditionally stable numerical scheme for the three-dimensional modified Fisher–Kolmogorov–Petrovsky–Piskunov equation

Seungyoon Kang, Soobin Kwak, Youngjin Hwang and Junseok Kim
Journal of Computational and Applied Mathematics 457 116273 (2025)
https://doi.org/10.1016/j.cam.2024.116273

Mathematical modelling and analysis of the adaptive dynamics in mosquito populations: uniform persistence of malaria infection

Bassirou Diop, Arnaud Ducrot and Ousmane Seydi
Journal of Mathematical Biology 90 (4) (2025)
https://doi.org/10.1007/s00285-025-02206-z

The evolution problem for the 1D nonlocal Fisher-KPP equation with a top hat kernel. Part 1. The Cauchy problem on the real line

David John Needham, John Billingham, Nikolaos Michael Ladas and John Meyer
European Journal of Applied Mathematics 1 (2024)
https://doi.org/10.1017/S0956792524000688

Well-Posedness and Regularity of Solutions to Neural Field Problems with Dendritic Processing

Daniele Avitabile, Nikolai V. Chemetov and P. M. Lima
Journal of Nonlinear Science 34 (4) (2024)
https://doi.org/10.1007/s00332-024-10055-1

Diffusion-Driven Blow-Up for a Nonlocal Fisher-KPP Type Model

Nikos I. Kavallaris, Evangelos Latos and Takashi Suzuki
SIAM Journal on Mathematical Analysis 55 (3) 2411 (2023)
https://doi.org/10.1137/21M145519X

Deep learning approximations for non-local nonlinear PDEs with Neumann boundary conditions

Victor Boussange, Sebastian Becker, Arnulf Jentzen, Benno Kuckuck and Loïc Pellissier
Partial Differential Equations and Applications 4 (6) (2023)
https://doi.org/10.1007/s42985-023-00244-0

Existence and Dynamics of Strains in a Nonlocal Reaction-Diffusion Model of Viral Evolution

Nikolai Bessonov, Gennady Bocharov, Andreas Meyerhans, Vladimir Popov and Vitaly Volpert
SIAM Journal on Applied Mathematics 81 (1) 107 (2021)
https://doi.org/10.1137/19M1282234

An efficient spectral-Galerkin method for solving two-dimensional nonlinear system of advection–diffusion–reaction equations

Farhad Fakhar-Izadi
Engineering with Computers 37 (2) 975 (2021)
https://doi.org/10.1007/s00366-019-00867-1

Periodic traveling waves and asymptotic spreading of a monostable reaction-diffusion equations with nonlocal effects

Bang-Sheng Han, De-Yu Kong Kong, Qihong Shi and Fan Wang
Electronic Journal of Differential Equations 2021 (01-104) 22 (2021)
https://doi.org/10.58997/ejde.2021.22

Propagating interface in reaction-diffusion equations with distributed delay

Haoyu Wang and Ge Tian
Electronic Journal of Differential Equations 2021 (01-104) 54 (2021)
https://doi.org/10.58997/ejde.2021.54

A Mathematical Study of the Influence of Hypoxia and Acidity on the Evolutionary Dynamics of Cancer

Giada Fiandaca, Marcello Delitala and Tommaso Lorenzi
Bulletin of Mathematical Biology 83 (7) (2021)
https://doi.org/10.1007/s11538-021-00914-3

Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains

Nikolai Bessonov, Gennady Bocharov, Andreas Meyerhans, Vladimir Popov and Vitaly Volpert
Mathematics 8 (1) 117 (2020)
https://doi.org/10.3390/math8010117

A probabilistic approach to Dirac concentration in nonlocal models of adaptation with several resources

Nicolas Champagnat and Benoit Henry
The Annals of Applied Probability 29 (4) (2019)
https://doi.org/10.1214/18-AAP1446

Dynamics of interfaces in the Fisher-KPP equation for slowly decaying initial data

Hirokazu Ninomiya and Eiji Yanagida
Journal of Differential Equations 267 (8) 4922 (2019)
https://doi.org/10.1016/j.jde.2019.05.021

Time-asymptotic convergence rates towards discrete steady states of a nonlocal selection-mutation model

Wenli Cai, Pierre-Emmanuel Jabin and Hailiang Liu
Mathematical Models and Methods in Applied Sciences 29 (11) 2063 (2019)
https://doi.org/10.1142/S0218202519500404

Dynamical effects of nonlocal interactions in discrete-time growth-dispersal models with logistic-type nonlinearities

Ozgur Aydogmus, Yun Kang, Musa Emre Kavgaci and Huseyin Bereketoglu
Ecological Complexity 31 88 (2017)
https://doi.org/10.1016/j.ecocom.2017.04.001

A finite volume method for nonlocal competition-mutation equations with a gradient flow structure

Wenli Cai and Hailiang Liu
ESAIM: Mathematical Modelling and Numerical Analysis 51 (4) 1223 (2017)
https://doi.org/10.1051/m2an/2016058

Doubly nonlocal reaction–diffusion equations and the emergence of species

M. Banerjee, V. Vougalter and V. Volpert
Applied Mathematical Modelling 42 591 (2017)
https://doi.org/10.1016/j.apm.2016.10.041

Traveling wave solutions in a nonlocal reaction-diffusion population model

Bang-Sheng Han and Zhi-Cheng Wang
Communications on Pure and Applied Analysis 15 (3) 1057 (2016)
https://doi.org/10.3934/cpaa.2016.15.1069

Traveling wave solutions in a nonlocal reaction-diffusion population model

Bang-Sheng Han and Zhi-Cheng Wang
Communications on Pure and Applied Analysis 15 (3) 1057 (2016)
https://doi.org/10.3934/cpaa.2016.15.1057

Preface to the Issue Nonlocal Reaction-Diffusion Equations

M. Alfaro, N. Apreutesei, F. Davidson, et al.
Mathematical Modelling of Natural Phenomena 10 (6) 1 (2015)
https://doi.org/10.1051/mmnp/201510601

On bounded positive stationary solutions for a nonlocal Fisher–KPP equation

Franz Achleitner and Christian Kuehn
Nonlinear Analysis: Theory, Methods & Applications 112 15 (2015)
https://doi.org/10.1016/j.na.2014.09.004

Patterns and Transitions to Instability in an Intraspecific Competition Model with Nonlocal Diffusion and Interaction

O. Aydogmus, M. Alfaro, N. Apreutesei, F. Davidson and V. Volpert
Mathematical Modelling of Natural Phenomena 10 (6) 17 (2015)
https://doi.org/10.1051/mmnp/201510603

Patterns for Competing Populations with Species Specific Nonlocal Coupling

A. Bayliss, V. A. Volpert, M. Alfaro, et al.
Mathematical Modelling of Natural Phenomena 10 (6) 30 (2015)
https://doi.org/10.1051/mmnp/201510604

A Nagumo-type model for competing populations with nonlocal coupling

M.C. Tanzy, V.A. Volpert, A. Bayliss and M.E. Nehrkorn
Mathematical Biosciences 263 70 (2015)
https://doi.org/10.1016/j.mbs.2015.01.014

Pattern formation in terms of semiclassically limited distribution on lower dimensional manifolds for the nonlocal Fisher–Kolmogorov–Petrovskii–Piskunov equation

E A Levchenko, A V Shapovalov and A Yu Trifonov
Journal of Physics A: Mathematical and Theoretical 47 (2) 025209 (2014)
https://doi.org/10.1088/1751-8113/47/2/025209

Stability and pattern formation for competing populations with asymmetric nonlocal coupling

M.C. Tanzy, V.A. Volpert, A. Bayliss and M.E. Nehrkorn
Mathematical Biosciences 246 (1) 14 (2013)
https://doi.org/10.1016/j.mbs.2013.09.002

Analysis of meshless local radial point interpolation (MLRPI) on a nonlinear partial integro-differential equation arising in population dynamics

Elyas Shivanian
Engineering Analysis with Boundary Elements 37 (12) 1693 (2013)
https://doi.org/10.1016/j.enganabound.2013.10.002

Dispersal, Individual Movement and Spatial Ecology

Vitaly Volpert and Vitali Vougalter
Lecture Notes in Mathematics, Dispersal, Individual Movement and Spatial Ecology 2071 331 (2013)
https://doi.org/10.1007/978-3-642-35497-7_12

An efficient pseudo‐spectral Legendre–Galerkin method for solving a nonlinear partial integro‐differential equation arising in population dynamics

Farhad Fakhar‐Izadi and Mehdi Dehghan
Mathematical Methods in the Applied Sciences 36 (12) 1485 (2013)
https://doi.org/10.1002/mma.2698

Properness and Topological Degree for Nonlocal Reaction‐Diffusion Operators

N. Apreutesei, V. Volpert and Nobuyuki Kenmochi
Abstract and Applied Analysis 2011 (1) (2011)
https://doi.org/10.1155/2011/629692

The evolutionary limit for models of populations interacting competitively via several resources

Nicolas Champagnat and Pierre-Emmanuel Jabin
Journal of Differential Equations 251 (1) 176 (2011)
https://doi.org/10.1016/j.jde.2011.03.007

Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations

Alexander Lorz, Sepideh Mirrahimi and Benoît Perthame
Communications in Partial Differential Equations 36 (6) 1071 (2011)
https://doi.org/10.1080/03605302.2010.538784

AN IN VITRO CELL POPULATION DYNAMICS MODEL INCORPORATING CELL SIZE, QUIESCENCE, AND CONTACT INHIBITION

ARNAUD DUCROT, FRANK LE FOLL, PIERRE MAGAL, HIDEKI MURAKAWA, JENNIFER PASQUIER and GLENN F. WEBB
Mathematical Models and Methods in Applied Sciences 21 (supp01) 871 (2011)
https://doi.org/10.1142/S0218202511005404

Pattern formation in a predator-prey system characterized by a spatial scale of interaction

E. Brigatti, M. Oliva, M. Núñez-López, R. Oliveros-Ramos and J. Benavides
EPL (Europhysics Letters) 88 (6) 68002 (2009)
https://doi.org/10.1209/0295-5075/88/68002

The non-local Fisher–KPP equation: travelling waves and steady states

Henri Berestycki, Grégoire Nadin, Benoit Perthame and Lenya Ryzhik
Nonlinearity 22 (12) 2813 (2009)
https://doi.org/10.1088/0951-7715/22/12/002