Asymptotic spreading for general heterogeneous Fisher-KPP type equations:
"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-KP...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Mathematical Society
2022
|
| Schriftenreihe: | Memoirs of the American Mathematical Society
Volume 280, Number 1381 (fourth of 8 numbers) |
| Schlagworte: |
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
> Spectral theory and eigenvalue problems
> General topics in linear spectral theory
|
| Zusammenfassung: | "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"-- |
| Beschreibung: | Includes bibliographical references |
| Beschreibung: | vi, 100 Seiten Illustrationen, Diagramme |
| ISBN: | 9781470454296 |
Internformat
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| 100 | 1 | |a Berestycki, Henri |d 1951- |0 (DE-588)112689272 |4 aut | |
| 245 | 1 | 0 | |a Asymptotic spreading for general heterogeneous Fisher-KPP type equations |c Henri Berestycki ; Grégoire Nadin |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2022 | |
| 264 | 4 | |c © 2022 | |
| 300 | |a vi, 100 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v Volume 280, Number 1381 (fourth of 8 numbers) | |
| 500 | |a Includes bibliographical references | ||
| 520 | 3 | |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"-- | |
| 653 | 0 | |a Reaction-diffusion equations | |
| 653 | 0 | |a Differential equations, Parabolic / Asymptotic theory | |
| 653 | 0 | |a Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions | |
| 653 | 0 | |a Partial differential equations -- Qualitative properties of solutions -- Homogenization; equations in media with periodic structure | |
| 653 | 0 | |a Partial differential equations -- Parabolic equations and systems -- Reaction-diffusion equations | |
| 653 | 0 | |a Partial differential equations -- Qualitative properties of solutions -- Maximum principles | |
| 653 | 0 | |a Partial differential equations -- Parabolic equations and systems -- Second-order parabolic equations | |
| 653 | 0 | |a Partial differential equations -- Spectral theory and eigenvalue problems -- General topics in linear spectral theory | |
| 653 | 0 | |a Operator theory -- Special classes of linear operators -- Positive operators and order-bounded operators | |
| 653 | 0 | |a Calculus of variations and optimal control; optimization -- Hamilton-Jacobi theories, including dynamic programming -- Viscosity solutions | |
| 700 | 1 | |a Nadin, Grégoire |0 (DE-588)1299393152 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4704-7281-8 |
| 830 | 0 | |a Memoirs of the American Mathematical Society |v Volume 280, Number 1381 (fourth of 8 numbers) |w (DE-604)BV008000141 |9 1381 | |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-034058845 | ||
Datensatz im Suchindex
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| author | Berestycki, Henri 1951- Nadin, Grégoire |
| author_GND | (DE-588)112689272 (DE-588)1299393152 |
| author_facet | Berestycki, Henri 1951- Nadin, Grégoire |
| author_role | aut aut |
| author_sort | Berestycki, Henri 1951- |
| author_variant | h b hb g n gn |
| building | Verbundindex |
| bvnumber | BV048684538 |
| ctrlnum | (OCoLC)1365567357 (DE-599)KXP1832134156 |
| dewey-full | 515/.3534 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.3534 |
| dewey-search | 515/.3534 |
| dewey-sort | 3515 43534 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV048684538 |
| illustrated | Illustrated |
| index_date | 2024-07-03T21:26:11Z |
| indexdate | 2024-07-10T09:46:02Z |
| institution | BVB |
| isbn | 9781470454296 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034058845 |
| oclc_num | 1365567357 |
| open_access_boolean | |
| owner | DE-29T DE-83 DE-355 DE-BY-UBR DE-11 |
| owner_facet | DE-29T DE-83 DE-355 DE-BY-UBR DE-11 |
| physical | vi, 100 Seiten Illustrationen, Diagramme |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Berestycki, Henri 1951- (DE-588)112689272 aut Asymptotic spreading for general heterogeneous Fisher-KPP type equations Henri Berestycki ; Grégoire Nadin Providence, RI American Mathematical Society 2022 © 2022 vi, 100 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society Volume 280, Number 1381 (fourth of 8 numbers) Includes bibliographical references "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"-- 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 Nadin, Grégoire (DE-588)1299393152 aut Erscheint auch als Online-Ausgabe 978-1-4704-7281-8 Memoirs of the American Mathematical Society Volume 280, Number 1381 (fourth of 8 numbers) (DE-604)BV008000141 1381 |
| spellingShingle | Berestycki, Henri 1951- Nadin, Grégoire Asymptotic spreading for general heterogeneous Fisher-KPP type equations Memoirs of the American Mathematical Society |
| title | Asymptotic spreading for general heterogeneous Fisher-KPP type equations |
| title_auth | Asymptotic spreading for general heterogeneous Fisher-KPP type equations |
| title_exact_search | Asymptotic spreading for general heterogeneous Fisher-KPP type equations |
| title_exact_search_txtP | Asymptotic spreading for general heterogeneous Fisher-KPP type equations |
| title_full | Asymptotic spreading for general heterogeneous Fisher-KPP type equations Henri Berestycki ; Grégoire Nadin |
| title_fullStr | Asymptotic spreading for general heterogeneous Fisher-KPP type equations Henri Berestycki ; Grégoire Nadin |
| title_full_unstemmed | Asymptotic spreading for general heterogeneous Fisher-KPP type equations Henri Berestycki ; Grégoire Nadin |
| title_short | Asymptotic spreading for general heterogeneous Fisher-KPP type equations |
| title_sort | asymptotic spreading for general heterogeneous fisher kpp type equations |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT berestyckihenri asymptoticspreadingforgeneralheterogeneousfisherkpptypeequations AT nadingregoire asymptoticspreadingforgeneralheterogeneousfisherkpptypeequations |