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Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on Mathbb{R}
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 init...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Providence :
American Mathematical Society,
2020.
|
| Series: | Memoirs of the American Mathematical Society ;
no. 1278. |
| Subjects: | |
| Online Access: |
Full text (Wentworth users only) |
| Local Note: | ProQuest Ebook Central |
MARC
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| 100 | 1 | |a Poláčik, Peter. | |
| 245 | 1 | 0 | |a Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on Mathbb{R} |h [electronic resource]. |
| 260 | |a Providence : |b American Mathematical Society, |c 2020. | ||
| 300 | |a 1 online resource (100 p.). | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v.264 | |
| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 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 | |
| 505 | 8 | |a 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 | |a 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. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Reaction-diffusion equations. | |
| 650 | 0 | |a Differential equations, Parabolic. | |
| 650 | 0 | |a Differential equations, Partial. | |
| 758 | |i has work: |a Propagating terraces and the dynamics of front -like solutions of reaction-diffusion equations ... on mathbb r (Text) |1 https://id.oclc.org/worldcat/entity/E39PD3vjkpFDdqtthfdqCMwgrq |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Poláčik, Peter |t Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on Mathbb{R} |d Providence : American Mathematical Society,c2020 |z 9781470441128 |
| 830 | 0 | |a Memoirs of the American Mathematical Society ; |v no. 1278. | |
| 852 | |b Ebooks |h ProQuest | ||
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| 880 | 8 | |6 505-00/(S |a 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 | |
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