LEADER 05860nam 22007093 450 001 9910967107303321 005 20251117113952.0 010 $a9781470472818 010 $a1470472813 035 $a(MiAaPQ)EBC30222570 035 $a(Au-PeEL)EBL30222570 035 $a(CKB)25289765000041 035 $a(OCoLC)1350685444 035 $a(EXLCZ)9925289765000041 100 $a20221110d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAsymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations 205 $a1st ed. 210 1$aProvidence :$cAmerican Mathematical Society,$d2022. 210 4$dİ2022. 215 $a1 online resource (112 pages) 225 1 $aMemoirs of the American Mathematical Society ;$vv.280 311 08$aPrint version: Berestycki, Henri Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations Providence : American Mathematical Society,c2022 9781470454296 327 $aA general formula for the expansion sets -- Exact asymptotic spreading speed in different frameworks -- Properties of the generalized principal eigenvalues -- Proof of the spreading property -- The homogeneous, periodic and compactly supported cases -- The almost periodic case -- The uniquely ergodic case -- The radially periodic case -- The space-independent case -- The directionally homogeneous case -- Proof of the spreading property with the alternative definition of the expansion sets and applications -- Further examples and other open problems. 330 $a"In this monograph, we review the theory and establish new and general results regarding spreading properties for heterogeneous reaction-diffusion equations. These are concerned with the dynamics of the solution starting from initial data with compact support. The nonlinearity f is of Fisher-KPP type, and admits 0 as an unstable steady state and 1 as a globally attractive one (or, more generally, admits entire solutions , where is unstable and is globally attractive). Here, the coefficients are only assumed to be uniformly elliptic, continuous and bounded in . To describe the spreading dynamics, we construct two non-empty star-shaped compact sets such that for all compact set (resp. all closed set , one has lim . The characterizations of these sets involve two new notions of generalized principal eigenvalues for linear parabolic operators in unbounded domains. In particular, it allows us to show that and to establish an exact asymptotic speed of propagation in various frameworks. These include: almost periodic, asymptotically almost periodic, uniquely ergodic, slowly varying, radially periodic and random stationary ergodic equations. In dimension N, if the coefficients converge in radial segments, again we show that and this set is characterized using some geometric optics minimization problem. Lastly, we construct an explicit example of non-convex expansion sets"--$cProvided by publisher. 410 0$aMemoirs of the American Mathematical Society 606 $aReaction-diffusion equations 606 $aDifferential equations, Parabolic$xAsymptotic theory 606 $aPartial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions$2msc 606 $aPartial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure$2msc 606 $aPartial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations$2msc 606 $aPartial differential equations -- Qualitative properties of solutions -- Maximum principles$2msc 606 $aPartial differential equations -- Parabolic equations and systems -- Second-order parabolic equations$2msc 606 $aPartial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory$2msc 606 $aOperator theory -- Special classes of linear operators -- Positive operators and order-bounded operators$2msc 606 $aCalculus of variations and optimal control; optimization -- Hamilton-Jacobi theories, including dynamic programming -- Viscosity solutions$2msc 615 0$aReaction-diffusion equations. 615 0$aDifferential equations, Parabolic$xAsymptotic theory. 615 7$aPartial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions. 615 7$aPartial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure. 615 7$aPartial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations. 615 7$aPartial differential equations -- Qualitative properties of solutions -- Maximum principles. 615 7$aPartial differential equations -- Parabolic equations and systems -- Second-order parabolic equations. 615 7$aPartial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory. 615 7$aOperator theory -- Special classes of linear operators -- Positive operators and order-bounded operators. 615 7$aCalculus of variations and optimal control; optimization -- Hamilton-Jacobi theories, including dynamic programming -- Viscosity solutions. 676 $a515/.3534 676 $a515.3534 686 $a35B40$a35B27$a35K57$a35B50$a35K10$a35P05$a47B65$a49L25$2msc 700 $aBerestycki$b H$g(Henri)$042307 701 $aNadin$b Gregoire$01802098 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910967107303321 996 $aAsymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations$94347629 997 $aUNINA