Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on (Record no. 18132)
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| 000 -LEADER | |
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| fixed length control field | 04474nam a22004453i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC6195961 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114250.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2020 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470458065 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470441128 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC6195961 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL6195961 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1154528262 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA377 |
| Item number | .P653 2020 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 515/.3534 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Poláčik, Peter. |
| 245 10 - TITLE STATEMENT | |
| Title | Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on |
| -- | Mathbb{R} |
| -- | |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2020. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2020. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (100 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society Series ; |
| Volume/sequential designation | v.264 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Main results -- 2.1. Minimal systems of waves and propagating terraces -- 2.2. The case where 0 and are both stable -- 2.3. The case where one of the steady states 0, is unstable -- 2.4. The \om-limit set and quasiconvergence -- 2.5. Locally uniform convergence to a specific front and exponential convergence -- Chapter 3. Phase plane analysis -- 3.1. Basic properties of the trajectories -- 3.2. A more detailed description of the minimal system of waves -- 3.3. Some trajectories out of the minimal system of waves -- Chapter 4. Proofs of Propositions 2.8, 2.12 -- Chapter 5. Preliminaries on the limit sets and zero number -- 5.1. Properties of Ω( ) -- 5.2. Zero number -- Chapter 6. Proofs of the main theorems -- 6.1. Some estimates: behavior at =±∞ and propagation -- 6.2. A key lemma: no intersection of spatial trajectories -- 6.3. The spatial trajectories of the functions in \Om( ) -- 6.4. \Om( ) contains the minimal propagating terrace -- 6.5. Ruling out other points from _{\Om}( ) -- 6.6. Completion of the proofs of Theorems 2.5, 2.13, and 2.15 -- 6.7. Completion of the proofs of Theorems 2.7, 2.9, 2.17 -- 6.8. Completion of the proofs of Theorems 2.11 and 2.19 -- 6.9. Proof of Theorem 2.22 -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | The author considers semilinear parabolic equations of the form u_t=u_xx+f(u),\quad x\in \mathbb R,t>0, where f a C^1 function. Assuming that 0 and \gamma >0 are constant steady states, the author investigates the large-time behavior of the front-like solutions, that is, solutions u whose initial values u(x,0) are near \gamma for x\approx -\infty and near 0 for x\approx \infty . If the steady states 0 and \gamma are both stable, the main theorem shows that at large times, the graph of u(\cdot ,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(\cdot ,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, \gamma is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their \omega -limit sets with respect to the locally uniform convergence consist of steady states. In the author's proofs he employs phase plane analysis, intersection comparison (or, zero number) arguments, and a geometric method involving the spatial trajectories \{(u(x,t),u_x(x,t)):x\in \mathbb R\}, t>0, of the solutions in question. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Partial differential equations -- Qualitative properties of solutions -- Stability. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Poláčik, Peter |
| Title | Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on |
| -- | Mathbb{R} |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2020 |
| International Standard Book Number | 9781470441128 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6195961">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=6195961</a> |
| Public note | Click to View |
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