Nonlocal Reaction–Diffusion Equations in Biomedical Applications

, , &
Acta Biotheoretica 70 (2):1-28 (2022)
  Copy   BIBTEX

Abstract

Nonlocal reaction–diffusion equations describe various biological and biomedical applications. Their mathematical properties are essentially different in comparison with the local equations, and this difference can lead to important biological implications. This review will present the state of the art in the investigation of nonlocal reaction–diffusion models in biomedical applications. We will consider various models arising in mathematical immunology, neuroscience, cancer modelling, and we will discuss their mathematical properties, nonlinear dynamics, resulting spatiotemporal patterns and biological significance.

Categories

Add categories

Keywords

Reprint years

DOI

10.1007/s10441-022-09436-4

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,164

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Trial Equation Method Based on Symmetry and Applications to Nonlinear Equations Arising in Mathematical Physics.Cheng-Shi Liu - 2011 - Foundations of Physics 41 (5):793-804.
A class of reaction-diffusion mechanisms which preferentially select striped patterns.Michael Lyons & Lionel G. Harrison - 1991 - Chemical Physics Letters 183 (1,2):158-164.
Hidden Variables with Nonlocal Time.Hrvoje Nikolić - 2012 - Foundations of Physics 42 (5):632-646.
Classical electrodynamics with nonlocal constitutive equations.George B. Cvijanovich - 1977 - Foundations of Physics 7 (11-12):785-799.
On Some Considerations of Mathematical Physics: May we Identify Clifford Algebra as a Common Algebraic Structure for Classical Diffusion and Schrödinger Equations?Elio Conte - 2012 - Advanced Studies in Theoretical Physics 6 (26):1289-1307.
Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory.Ruofeng Rao & Shouming Zhong - 2017 - Complexity:1-9.
Large time behavior for convection-diffusion equations in IRN with asymptotically constant diffusion.Gema Duro & Enrique Zuazua - 1999 - History and Philosophy of Logic 24 (7-8):1283-1340.
Black-Scholes PDE: A Finance Application.Quan-Hoang Vuong - 2001 - In International Conference on Differential Equations, Approximations and Applications, DEAA - 2001. pp. 53-53.
Two Mathematically Equivalent Versions of Maxwell’s Equations.Tepper L. Gill & Woodford W. Zachary - 2011 - Foundations of Physics 41 (1):99-128.
Chemical morphogenesis: Turing patterns in an experimental chemical system.E. Dulos, J. Boissonade, J. J. Perraud, B. Rudovics & P. De Kepper - 1996 - Acta Biotheoretica 44 (3-4):249-261.
Self-diffusion of aluminium in the intermetallic compound Fe-48 at.% Al.Ryusuke Nakamura & Yoshiaki Iijima - 2003 - Philosophical Magazine 83 (4):477-483.
Chemical morphogenesis: Turing patterns in an experimental chemical system.E. Dulos, J. Boissonade, J. J. Perraud, B. Rudovics & P. Kepper - 1996 - Acta Biotheoretica 44 (3-4).
Evaluation of the thermodynamic models for the thermal diffusion factor.Mariana Gonzalez-Bagnoli, Alexander Shapiro & Erling Stenby - 2003 - Philosophical Magazine 83 (17-18):2171-2183.
A diffusion model for mesoderm induction in amphibian embryos.C. J. Weyer, P. D. Nieuwkoop & A. Lindenmayer - 1977 - Acta Biotheoretica 26 (3):164-180.
Selection rules, causality, and unitarity in statistical and quantum physics.A. Kyrala - 1974 - Foundations of Physics 4 (1):31-51.

Analytics

Added to PP
2022-03-18

Downloads
28 (#536,385)

6 months
5 (#526,961)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

No citations found.

Add more citations

References found in this work

Ernst Mayr and the modern concept of species.Kevin de Queiroz - 2005 - Proceedings of the National Academy of Sciences of the United States of America 102 (1):6600-6607.

Add more references