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010 a| 2022048348;

020 a| 9781470454296q| (paperback);

020 z| 9781470472818q| (epub);

035 a| (WaSeSS)ssj0002762353;

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084 a| 35B40a| 35B27a| 35K57a| 35B50a| 35K10a| 35P05a| 47B65a| 49L252| msc;

100 1 a| Berestycki, H.q| (Henri)?| UNAUTHORIZED;

245 10 a| Asymptotic spreading for general heterogeneous Fisher-KPP type equationsh| [electronic resource] /c| Henri Berestycki, Grégoire Nadin.;

260 a| Providence, RI :b| American Mathematical Society,c| [2022];

300 a| vi, 100 pages ;c| 26 cm.;

490 0 a| Memoirs of the American Mathematical Society ;v| number 1381;

504 a| Includes bibliographical references (pages 95-100).;

505 0 a| A 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.;

506 a| Available only to authorized users.;

520 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"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Reaction-diffusion equations.=| ^A282077;

650 0 a| Differential equations, Parabolicx| Asymptotic theory.=| ^A417037;

650 7 a| Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions.2| msc;

650 7 a| Partial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure.2| msc;

650 7 a| Partial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations.2| msc;

650 7 a| Partial differential equations -- Qualitative properties of solutions -- Maximum principles.2| msc;

650 7 a| Partial differential equations -- Parabolic equations and systems -- Second-order parabolic equations.2| msc;

650 7 a| Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory.2| msc;

650 7 a| Operator theory -- Special classes of linear operators -- Positive operators and order-bounded operators.2| msc;

650 7 a| Calculus of variations and optimal control; optimization -- Hamilton-Jacobi theories, including dynamic programming -- Viscosity solutions.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Nadin, Grégoire.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=30222570;

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Asymptotic spreading for general heterogeneous Fisher-KPP type equations / Henri Berestycki, Grégoire Nadin.

Author/creator	Berestycki, H.
Other author	Nadin, Grégoire.
Format	Electronic
Publication Info	Providence, RI : American Mathematical Society, [2022]
Description	vi, 100 pages ; 26 cm.
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Reaction-diffusion equations. Differential equations, Parabolic--Asymptotic theory.

Series	Memoirs of the American Mathematical Society ; number 1381
Contents	A 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.
Abstract	"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"-- Provided by publisher.
Bibliography note	Includes bibliographical references (pages 95-100).
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022048348
ISBN	9781470454296 (paperback)
ISBN	(epub)

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Asymptotic spreading for general heterogeneous Fisher-KPP type equations / Henri Berestycki, Grégoire Nadin.

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