LEADER 01121nam 2200397 450 001 9910795407503321 005 20230814215513.0 010 $a1-68325-451-1 035 $a(CKB)4340000000260279 035 $a(MiAaPQ)EBC5321024 035 $a(Au-PeEL)EBL5321024 035 $a(CaPaEBR)ebr11524761 035 $a(OCoLC)1029500164 035 $a(EXLCZ)994340000000260279 100 $a20180403h20182018 uy 0 101 0 $ager 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$a1000 Aquarelle von genialen Meistern /$fVictoria Charles 210 1$aNew York :$cParkstone International,$d[2018] 210 4$dŠ[2018] 215 $a1 online resource (544 pages) $ccolor illustrations 311 $a1-78525-016-7 606 $aWatercolor painting 615 0$aWatercolor painting. 676 $a751.42 700 $aCharles$b Victoria$0597104 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910795407503321 996 $a1000 Aquarelle von genialen Meistern$93685952 997 $aUNINA LEADER 04816nam 22008175 450 001 9910917797703321 005 20250523181722.0 010 $a9783031777721 010 $a3031777727 024 7 $a10.1007/978-3-031-77772-1 035 $a(CKB)37037002400041 035 $a(MiAaPQ)EBC31849657 035 $a(Au-PeEL)EBL31849657 035 $a(DE-He213)978-3-031-77772-1 035 $a(EXLCZ)9937037002400041 100 $a20241218d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Dynamics of Front Propagation in Nonlocal Reaction?Diffusion Equations /$fby Jean-Michel Roquejoffre 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (210 pages) 225 1 $aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4797 311 08$a9783031777714 311 08$a3031777719 327 $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. 330 $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. . 410 0$aLecture Notes on Mathematical Modelling in the Life Sciences,$x2193-4797 606 $aBiomathematics 606 $aEvolution (Biology) 606 $aPopulation genetics 606 $aMathematics 606 $aMathematical analysis 606 $aDynamics 606 $aMathematical and Computational Biology 606 $aEvolutionary Biology 606 $aPopulation Genetics 606 $aApplications of Mathematics 606 $aAnalysis 606 $aDynamical Systems 606 $aBiomatemātica$2thub 606 $aAnālisi matemātica$2thub 606 $aEvoluciķ (Biologia)$2thub 608 $aLlibres electrōnics$2thub 615 0$aBiomathematics. 615 0$aEvolution (Biology) 615 0$aPopulation genetics. 615 0$aMathematics. 615 0$aMathematical analysis. 615 0$aDynamics. 615 14$aMathematical and Computational Biology. 615 24$aEvolutionary Biology. 615 24$aPopulation Genetics. 615 24$aApplications of Mathematics. 615 24$aAnalysis. 615 24$aDynamical Systems. 615 7$aBiomatemātica 615 7$aAnālisi matemātica 615 7$aEvoluciķ (Biologia) 676 $a570.285 700 $aRoquejoffre$b Jean-Michel$01780671 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910917797703321 996 $aThe Dynamics of Front Propagation in Nonlocal Reaction?Diffusion Equations$94306398 997 $aUNINA