Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R

Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R
Author :
Publisher : American Mathematical Soc.
Total Pages : 100
Release :
ISBN-10 : 9781470441128
ISBN-13 : 1470441128
Rating : 4/5 (28 Downloads)

Book Synopsis Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R by : Peter Poláčik

Download or read book Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R written by Peter Poláčik and published by American Mathematical Soc.. This book was released on 2020-05-13 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>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 γ for x≈−∞ and near 0 for x≈∞. If the steady states 0 and γ are both stable, the main theorem shows that at large times, the graph of u(⋅,t) is arbitrarily close to a propagating terrace (a system of stacked traveling fonts). The author proves this result without requiring monotonicity of u(⋅,0) or the nondegeneracy of zeros of f. The case when one or both of the steady states 0, γ is unstable is considered as well. As a corollary to the author's theorems, he shows that all front-like solutions are quasiconvergent: their ω-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),ux(x,t)):x∈R}, t>0, of the solutions in question.


Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R Related Books

Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on R
Language: en
Pages: 100
Authors: Peter Poláčik
Categories: Education
Type: BOOK - Published: 2020-05-13 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The author considers semilinear parabolic equations of the form ut=uxx+f(u),x∈R,t>0, where f a C1 function. Assuming that 0 and γ>0 are constant steady state
Propagating Terraces and the Dynamics of Front-Like Solutions of Reaction-Diffusion Equations on Mathbb{R}
Language: en
Pages: 87
Authors: Peter Poláčik
Categories: Electronic books
Type: BOOK - Published: 2020 - Publisher:

DOWNLOAD EBOOK

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 ar
Patterns of Dynamics
Language: en
Pages: 411
Authors: Pavel Gurevich
Categories: Mathematics
Type: BOOK - Published: 2018-02-07 - Publisher: Springer

DOWNLOAD EBOOK

Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volum
Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
Language: en
Pages: 170
Authors: Jacob Bedrossian
Categories: Mathematics
Type: BOOK - Published: 2020-09-28 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove
Global Smooth Solutions for the Inviscid SQG Equation
Language: en
Pages: 102
Authors: Angel Castro
Categories: Mathematics
Type: BOOK - Published: 2020-09-28 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

In this paper, the authors show the existence of the first non trivial family of classical global solutions of the inviscid surface quasi-geostrophic equation.