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020 _a9783031777721
_9978-3-031-77772-1
024 7 _a10.1007/978-3-031-77772-1
_2doi
050 4 _aQH323.5
050 4 _aQH324.2-324.25
072 7 _aPBW
_2bicssc
072 7 _aPSA
_2bicssc
072 7 _aMAT003000
_2bisacsh
072 7 _aPSAX
_2thema
100 1 _aRoquejoffre, Jean-Michel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_989089
245 1 4 _aThe Dynamics of Front Propagation in Nonlocal Reaction–Diffusion Equations
_h[electronic resource] /
_cby Jean-Michel Roquejoffre.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIII, 200 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes on Mathematical Modelling in the Life Sciences,
_x2193-4797
505 0 _a- 1. Introduction -- 2. Cauchy Problem, Steady States, and Diffusive Behaviour -- 3. Travelling Waves -- 4. Sharp Fisher-KPP Spreading -- 5. Sharp ZFK Spreading -- 6. Spreading in Several Space Dimensions -- 7. Final Remarks.
520 _aThe book provides a self-contained and complete description of the long time evolution of the solutions to a class of one-dimensional reaction–diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation is the mathematical analysis of models for biological invasions. The model under study, while simple looking, is of current use in real-life situations. Interestingly, it arises in totally different contexts, such as the study of branching random walks in probability theory. While the model has attracted a lot of attention, and while many partial results about the time-asymptotic behaviour of its solutions have been proved over the last decades, some basic questions on the sharp asymptotics have remained unanswered. One ambition of this monograph is to close these gaps. In some of the situations that we envisage, the level sets organise themselves into an invasion front that is asymptotically linear in time, up to a correction that converges exponentially in time to a constant. In other situations that constitute the main and newest part of the work, the correction is asymptotically logarithmic in time. Despite these apparently different behaviours, there is an underlying common way of thinking that is underlined. At the end of each chapter, a long set of problems is proposed, many of them rather elaborate and suitable for master's projects or even the first question in a PhD thesis. Open questions are also discussed. The ideas presented in the book apply to more elaborate systems modelling biological invasions or the spatial propagation of epidemics. The models themselves may be multidimensional, but they all have in common a mechanism imposing the propagation in a given direction; examples are presented in the problems that conclude each chapter. These ideas should also be useful in the treatment of further models that we are not able to envisage for the time being. The book is suitable for graduate or PhD students as well as researchers. .
650 0 _aBiomathematics.
_970325
650 0 _aEvolution (Biology).
_964762
650 0 _aPopulation genetics.
_989090
650 0 _aMathematics.
_965523
650 0 _aMathematical analysis.
_964178
650 0 _aDynamical systems.
650 1 4 _aMathematical and Computational Biology.
_970327
650 2 4 _aEvolutionary Biology.
_966166
650 2 4 _aPopulation Genetics.
_989091
650 2 4 _aApplications of Mathematics.
_965529
650 2 4 _aAnalysis.
650 2 4 _aDynamical Systems.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031777714
776 0 8 _iPrinted edition:
_z9783031777738
830 0 _aLecture Notes on Mathematical Modelling in the Life Sciences,
_x2193-4797
_986185
856 4 0 _uhttps://doi.org/10.1007/978-3-031-77772-1
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c65795
_d65795