Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations

• Autore: Berestycki Henri
• Pubblicazione: Providence : , : American Mathematical Society, , 2022; ©2022
• Edizione: 1st ed.
• Descrizione fisica: 1 online resource (112 pages)
• Disciplina: 515/.3534; 515.3534
• Soggetto topico: Reaction-diffusion equations; Differential equations, Parabolic - Asymptotic theory; Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions; Partial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure; Partial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations; Partial differential equations -- Qualitative properties of solutions -- Maximum principles; Partial differential equations -- Parabolic equations and systems -- Second-order parabolic equations; Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory; Operator theory -- Special classes of linear operators -- Positive operators and order-bounded operators; Calculus of variations and optimal control; optimization -- Hamilton-Jacobi theories, including dynamic programming -- Viscosity solutions
• Classificazione: 35B4035B2735K5735B5035K1035P0547B6549L25
• Altri autori: NadinGrégoire
• Nota di contenuto: 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.
• Sommario/riassunto: "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"--
• Titolo autorizzato: Asymptotic Spreading for General Heterogeneous Fisher-KPP Type Equations
• ISBN: 9781470472818; 1470472813
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910967107303321
• Lo trovi qui: Univ. Federico II
• Serie: Memoirs of the American Mathematical Society