• Corpus ID: 221516421

Asymptotic Convergence of Solutions for One-Dimensional Keller-Segel Equations.

  title={Asymptotic Convergence of Solutions for One-Dimensional Keller-Segel Equations.},
  author={Satoru Iwasaki and Koichi Osaki and Atsushi Yagi},
  journal={arXiv: Analysis of PDEs},
The second and third authors of this paper have constructed in [14] finite-dimensional attractors for the one-dimensional Keller-Segel equations. They have also remarked in [14, Section 7] that, when the sensitivity function is a linear function, the equations admit a global Lyapunov function. But at that moment they could not show the asymptotic convergence of solutions. This paper is then devoted to supplementing the results of [14, Section 7] by showing that, as $t \to \infty$, every… 
Convergence to diffusion waves for solutions of 1D Keller-Segel model
In this paper, we are concerned with the asymptotic behavior of solutions to the Cauchy problem (or initial-boundary value problem) of one-dimensional Keller-Segel model. For the Cauchy problem, we


A Simple Unified Approach to Some Convergence Theorems of L. Simon
Abstract We give a new and easier proof for the convergences result of L. Simon [15] concerning global and bounded solutions of a heat equation with analytic nonlinearity. By constructing a new
Functional Analysis, Sobolev Spaces and Partial Differential Equations
Preface.- 1. The Hahn-Banach Theorems. Introduction to the Theory of Conjugate Convex Functions.- 2. The Uniform Boundedness Principle and the Closed Graph Theorem. Unbounded Operators. Adjoint.
Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
Soit Σ une variete de Riemann compacte et soit une fonction reguliere u=u(x,t), (x,t)∈ΣX(0,T) (T>0) satisfaisant une equation d'evolution soit de la forme ci-#7B-M(u)=f soit de la forme
We prove convergence to equilibrium of global and bounded solutions of gradient-like evolution equations. Our abstract results are illustrated by several examples in finite and infinite dimensions.
Real Sectorial Operators
Sectorial operators that act in complex Banach spaces and map real subspaces into themselves should be called real sectorial operators. These operators have already been used implicitly in the study
Introduction to Complex Analysis
Part 1 The complex plane: complex numbers open and closed sets in the complex plane limits and continuity. Part 2 Holomorphic function and power series: complex power series elementary functions.
An introduction to complex analysis in several variables
I. Analytic Functions of One Complex Variable. II. Elementary Properties of Functions of Several Complex Variables. III. Applications to Commutative Banach Algebras. IV. L2 Estimates and Existence