Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R
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Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R
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Author : Peter Poláčik
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-05-13
Propagating Terraces And The Dynamics Of Front Like Solutions Of Reaction Diffusion Equations On R written by Peter Poláčik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-13 with Education categories.
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.
The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations
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Author : Jean-Michel Roquejoffre
language : en
Publisher: Springer Nature
Release Date : 2024-12-18
The Dynamics Of Front Propagation In Nonlocal Reaction Diffusion Equations written by Jean-Michel Roquejoffre and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-18 with Mathematics categories.
The book provides a self-contained and complete description of the long time evolution of the solutions to a class of one-dimensional reaction–diffusion equations, in which the diffusion is given by an integral operator. The underlying motivation is the mathematical analysis of models for biological invasions. The model under study, while simple looking, is of current use in real-life situations. Interestingly, it arises in totally different contexts, such as the study of branching random walks in probability theory. While the model has attracted a lot of attention, and while many partial results about the time-asymptotic behaviour of its solutions have been proved over the last decades, some basic questions on the sharp asymptotics have remained unanswered. One ambition of this monograph is to close these gaps. In some of the situations that we envisage, the level sets organise themselves into an invasion front that is asymptotically linear in time, up to a correction that converges exponentially in time to a constant. In other situations that constitute the main and newest part of the work, the correction is asymptotically logarithmic in time. Despite these apparently different behaviours, there is an underlying common way of thinking that is underlined. At the end of each chapter, a long set of problems is proposed, many of them rather elaborate and suitable for master's projects or even the first question in a PhD thesis. Open questions are also discussed. The ideas presented in the book apply to more elaborate systems modelling biological invasions or the spatial propagation of epidemics. The models themselves may be multidimensional, but they all have in common a mechanism imposing the propagation in a given direction; examples are presented in the problems that conclude each chapter. These ideas should also be useful in the treatment of further models that we are not able to envisage for the time being. The book is suitable for graduate or PhD students as well as researchers.
Patterns Of Dynamics
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Author : Pavel Gurevich
language : en
Publisher: Springer
Release Date : 2018-02-07
Patterns Of Dynamics written by Pavel Gurevich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-07 with Mathematics categories.
Theoretical advances in dynamical-systems theory and their applications to pattern-forming processes in the sciences and engineering are discussed in this volume that resulted from the conference Patterns in Dynamics held in honor of Bernold Fiedler, in Berlin, July 25-29, 2016.The contributions build and develop mathematical techniques, and use mathematical approaches for prediction and control of complex systems. The underlying mathematical theories help extract structures from experimental observations and, conversely, shed light on the formation, dynamics, and control of spatio-temporal patterns in applications. Theoretical areas covered include geometric analysis, spatial dynamics, spectral theory, traveling-wave theory, and topological data analysis; also discussed are their applications to chemotaxis, self-organization at interfaces, neuroscience, and transport processes.
Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case
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Author : Jacob Bedrossian
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Dynamics Near The Subcritical Transition Of The 3d Couette Flow I Below Threshold Case written by Jacob Bedrossian and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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 that for sufficiently regular initial data of size $epsilon leq c_0mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t rightarrow infty $. For times $t gtrsim mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ``2.5 dimensional'' streamwise-independent solutions referred to as streaks.
Global Smooth Solutions For The Inviscid Sqg Equation
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Author : Angel Castro
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-09-28
Global Smooth Solutions For The Inviscid Sqg Equation written by Angel Castro and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-28 with Mathematics categories.
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.
Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms
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Author : Kazuyuki Hatada
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
Hecke Operators And Systems Of Eigenvalues On Siegel Cusp Forms written by Kazuyuki Hatada and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.
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The Irreducible Subgroups Of Exceptional Algebraic Groups
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Author : Adam R. Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-06-18
The Irreducible Subgroups Of Exceptional Algebraic Groups written by Adam R. Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-18 with Education categories.
This paper is a contribution to the study of the subgroup structure of excep-tional algebraic groups over algebraically closed fields of arbitrary characteristic. Following Serre, a closed subgroup of a semisimple algebraic group G is called irreducible if it lies in no proper parabolic subgroup of G. In this paper we com-plete the classification of irreducible connected subgroups of exceptional algebraic groups, providing an explicit set of representatives for the conjugacy classes of such subgroups. Many consequences of this classification are also given. These include results concerning the representations of such subgroups on various G-modules: for example, the conjugacy classes of irreducible connected subgroups are determined by their composition factors on the adjoint module of G, with one exception. A result of Liebeck and Testerman shows that each irreducible connected sub-group X of G has only finitely many overgroups and hence the overgroups of X form a lattice. We provide tables that give representatives of each conjugacy class of connected overgroups within this lattice structure. We use this to prove results concerning the subgroup structure of G: for example, when the characteristic is 2, there exists a maximal connected subgroup of G containing a conjugate of every irreducible subgroup A1 of G.
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators
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Author : Jonathan Gantner
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Operator Theory On One Sided Quaternion Linear Spaces Intrinsic S Functional Calculus And Spectral Operators written by Jonathan Gantner and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
Two major themes drive this article: identifying the minimal structure necessary to formulate quaternionic operator theory and revealing a deep relation between complex and quaternionic operator theory. The theory for quaternionic right linear operators is usually formulated under the assumption that there exists not only a right- but also a left-multiplication on the considered Banach space $V$. This has technical reasons, as the space of bounded operators on $V$ is otherwise not a quaternionic linear space. A right linear operator is however only associated with the right multiplication on the space and in certain settings, for instance on quaternionic Hilbert spaces, the left multiplication is not defined a priori, but must be chosen randomly. Spectral properties of an operator should hence be independent of the left multiplication on the space.
Theory Of Fundamental Bessel Functions Of High Rank
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Author : Zhi Qi
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Theory Of Fundamental Bessel Functions Of High Rank written by Zhi Qi and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals
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Author : Paul M Feehan
language : en
Publisher: American Mathematical Society
Release Date : 2021-02-10
Ojasiewicz Simon Gradient Inequalities For Coupled Yang Mills Energy Functionals written by Paul M Feehan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
The authors' primary goal in this monograph is to prove Łojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces that impose minimal regularity requirements on pairs of connections and sections.