Last edited by Tonos
Friday, May 1, 2020 | History

6 edition of Global attractors in abstract parabolic problems found in the catalog.

# Global attractors in abstract parabolic problems

Written in English

Subjects:
• Attractors (Mathematics),
• Differential equations, Parabolic.

• Edition Notes

Includes bibliographical references (p. 225-233) and index.

Classifications The Physical Object Statement Jan W. Cholewa & Tomasz Dlotko ; in cooperation with Nathaniel Chafee. Series London Mathematical Society lecture note series ;, 278 Contributions Dlotko, Tomasz., London Mathematical Society. LC Classifications QA614.813 .C48 2000 Pagination xii, 235 p. ; Number of Pages 235 Open Library OL6900309M ISBN 10 0521794242 LC Control Number 00710511 OCLC/WorldCa 44014677

dynamical system is global attractor of a semiﬂow. The ﬁrst construction of a global attractor for some dissipative PDEs was in the seminal work of Ladyzhenskaya [28] in , then the theory of global attractors was developed by Foias and Temam [20], Babin and Vishik [3] and Hale [22]. Generally speaking, global attractor is a com-Author: Junyi Tu. UDC Mathematics Subject Classification: primary 37L05; secondary 37L30, 37L This book provides an exhaustive introduction to the scopeFile Size: 2MB. An attractor is a subset A of the phase space characterized by the following three conditions. A is forward invariant under f: if a is an element of A then so is f(t,a), for all t > 0.; There exists a neighborhood of A, called the basin of attraction for A and denoted B(A), which consists of all points b that "enter A in the limit t → ∞". More formally, B(A) is the set of all points b in.   In order to construct global attractors, an approach based on the notion of generalized semiflow is employed instead of the usual semi-group approach, since solutions of the Cauchy problem for the equation might not be unique.

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### Global attractors in abstract parabolic problems by Jan W. Cholewa Download PDF EPUB FB2

In particular the theory of global attractors is presented in detail. Extensive auxiliary material and rich references make this self-contained book suitable as an introduction for graduate students, and experts from other areas, who wish to enter this by: Existence of a global attractor -- abstract setting -- Global solvability and attractors in X[superscript [alpha]] scales -- Ch.

Application of abstract results to parabolic equations -- Global Attractors in Abstract Parabolic Problems Book   January   with  89 Reads  How we measure 'reads' A 'read' is counted each time someone views a publication summary.

theory of attractors for extended (translation-invariant) parabolic problems, given for example in [3]. Compared with the classics by Hale, Henry or Temam [1, 2, 4], this book is certainly more focused, but it does not give as much to enthuse over.

Cholewa and Dlotko leave no room for speculations or open questions. These authors never raiseCited by:   Book reviews. GLOBAL ATTRACTORS IN ABSTRACT PARABOLIC PROBLEMS (London Mathematical Society Lecture Note Series ) Jacques Rougemont.

Heriot‐Watt University, Edinburgh. Search for more papers by this author. Jacques Author: Jacques Rougemont. Global Attractors in Abstract Parabolic Problems pdf By Ubaldo Garibaldi In this book the authors exploit these same ideas to investigate the asymptotic behavior of dynamical systems corresponding to parabolic equations.

Global attractors in abstract parabolic problems. By Jan W Cholewa and Tomasz Dlotko. Abstract. This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equationsAuthor: Jan W Cholewa and Tomasz Dlotko.

Global Attractors in Abstract Parabolic Problems的话题 (全部 条) 什么是话题 无论是一部作品、一个人，还是一件事，都往往可以衍生出许多不同的话题。. () Attractors for Parabolic Problems with Nonlinear Boundary Conditions.

Journal of Mathematical Analysis and Applications() Reaction-diffusion problems in cell by: 7. Robinson, Infinite-Dimensional Dynamical Systems: An Introduction to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge University Press, Google Scholar Cited by: 1.

Global existence and nonexistence of solutions with initial data in the potential well are derived. Moreover, by using the iteration technique for regularity estimates, we obtain that for any k ≥ 0, the semilinear parabolic possesses a global attractor in H k (Ω), which attracts any bounded subsets of H k (Ω) in the H k ‐ by: 1.

Get this from a library. Global attractors in abstract parabolic problems. [Jan W Cholewa; Tomasz Dlotko; London Mathematical Society.] -- This book investigates the asymptotic behaviour of dynamical systems corresponding to parabolic equations.

Existence of a global attractor - abstract setting 86 Global solvability and attractors in Xa scales 88 Chapter 5. Application of abstract results to parabolic equations 90 Formulation of the problem 90 Global Solutions via partial information 94 Existence of a global attractor. This paper is devoted to study the existence of global attractor in H-0(1)(Omega) and uniform bounds of it in L-infinity(Omega) for a class of parabolic problems with homogeneous boundary.

Kalita P. () On Global Attractor for Parabolic Partial Differential Inclusion and Its Time Semidiscretization. In: Hiriart-Urruty JB., Korytowski A., Maurer H., Szymkat M. (eds) Advances in Mathematical Modeling, Optimization and Optimal Control. Springer Optimization and Its Applications, vol Springer, Cham.

First Online 20 May Author: Piotr Kalita. (global attractors) of parabolic problems behave continuously with respect to perturbations of the equation.

This is done from a functional analytic point of view on general approxi-mation scheme. By continuity of attractors we understand upper and lower semicontinuity *Research partially supported by CNPq grant # /File Size: KB.

We mention, in particular, that the obtained result can be used to prove the existence of the global periodic attractor for abstract parabolic problems. In this paper we consider the existence of a global periodic attractor for a class of infinite dimensional dissipative equations under homogeneous Dirichlet boundary : Hongyan Li.

nique and the classical existence theorem of global attractors, we prove that the sixth order parabolic equation possesses a global attractor in the Hk (k 0) space, which attracts any bounded subset of Hk(Ω) in the Hk-norm.

Keywords: sixth order nonlinear parabolic equation, existence, attractors. MSC 35B41, 35K35, 35K 1. Introduction. Abstract: For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity.

We further show that a priori estimates in lower norms are sufficient for the existence of a global attractor Author: Martin Meyries.

Continuity of global attractors for a class of non local evolution equations. Discrete & Continuous Dynamical Systems - A,26 (3): doi: /dcds [2] John M. Ball. Global attractors for damped semilinear wave equations.

This book treats the theory of global attractors, a recent development in the theory of partial differential equations, in a way that also includes much of the traditional elements of the subject.

As such it gives a quick but directed introduction to some fundamental concepts, and by the end proceeds to current research by: Examples of global attractors in parabolic problems. Alexandre N. CARVALHO, Jan. CHOLEWA, and Tomasz DLOTKO Full-text: Open access. PDF File ( KB) Article info and citation; First page; Article information.

Source Hokkaido Math. J., Vol Number 1 (), Dates First Cited by: By means of a nonstandard estimation about the energy functional, the authors prove the existence of a global attractor for an abstract nonlinear evolution equation.

As an application, the existence of a global attractor for some nonlinear reaction-diffusion equations with some distribution derivatives in inhomogeneous terms is obtained. Attractors for parabolic problems in weighted spaces Xiaojun LI, Ying TANG School of Science, Hohai University, Nanjing, Jiangsu, P.R.

China Received: Accepted: Published Online: Printed: Abstract: The purpose of this paper is to investigate the asymptotic behavior of the solutions of parabolic equations. A class of scalar semilinear parabolic equations possessing absorbing sets, a Lyapunov functional, and a global attractor are considered.

The gradient structure of the problem Cited by: Attractors for Parabolic Problems with Nonlinear Boundary Conditions J.G. Ruas-FilhoGlobal attractors for parabolic problems in fractional power spaces.

Google Scholar. 9 A. Carvalho, A. Rodriguez Bernal, Upper semi-continuity of attractors for parabolic problems with localized large diffusion and nonlinear boundary by: In this paper we prove existence of global solutions and (L 2 (Ω) × L 2 (Γ), (H 1 (Ω) ∩ L p (Ω)) × L p (Γ))-global attractors for semilinear parabolic equations with dynamic boundary conditions in bounded domains with a smooth boundary, where there is no other restriction on p (≥ 2).Cited by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Abstract.

Global attractors and exponential attractors are constructed for some quasilinear parabolic equations. The construction for the exponential attractor is carried out within the framework of the method of ℓ-trajectories.

Introduction. Let Ω be a bounded open subset of Rn with smooth boundary ∂Ω. This book provides an overview of the state of the art in important subjects, including — besides elliptic and parabolic issues — geometry, free boundary problems, fluid mechanics, evolution problems in general, calculus of variations, homogenization, control, modeling and numerical analysis.

Global Attractors for Multivalued Flows. Abstract. We investigate the asymptotic behavior of solutions of a class of degenerate parabolic equations in a bounded domain () with a polynomial growth nonlinearity of arbitrary existence of global attractors is proved in, and, respectively, when can be Cited by: 1.

CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We consider global attractors A f of dissipative parabolic equations u t = u xx + f(x; u; u x) on the unit interval 0 x 1 with Neumann boundary conditions.

A permutation ß f is defined by the two orderings of the set of (hyperbolic) equilibrium solutions u t j 0 according to their respective values at the two. Global Attractors. Global Attractors In Abstract Parabolic Problems By Jan W.

Cholewa English Pap. $Rehabilitation In. Rehabilitation In Parkinson's Disease By Cholewa Joanna English Paperback Book.$ Developing And. Developing And Managing Physical Security Programs By John Cholewa English Pap.

This book deals with the long-time behavior of solutions of degenerate parabolic dissipative equations arising in the study of biological, ecological, and physical problems. Examples include porous media equations, $$p$$-Laplacian and doubly nonlinear equations, as well as degenerate diffusion equations with chemotaxis and ODE-PDE coupling systems.

[1] M. Aizenman, A sufficient condition for the avoidance of sets by measure preserving flows in $\mathbb R^n$, Duke Math. J., 45 (), doi: /S Google Scholar [2] C. Anh and P. Hung, Global attractors for a class of degenerate parabolic equations, Acta m., 34 (), Google ScholarCited by: 5.

Using the theory of uniform global attractors for multi-valued semiprocesses, we prove the existence of attractors for quasilinear parabolic equations related to Caffarelli-Kohn- Nirenberg inequalities, in which the conditions imposed on the nonlinearity provide the global existence of weak solutions but not uniqueness, in both autonomous and non-autonomous by: 1.

In this book international expert authors provide solutions for modern fundamental problems including the complexity of computing of critical points for set-valued mappings, the behaviour of solutions of ordinary differential equations, partial differential equations and difference equations, or the development of an abstract theory of global attractors for multi-valued impulsive dynamical.

The main aim of this book is to give more insight into such types of PDEs and to fill this gap. This aim is achieved by a systematic study of the well-posedness and the dynamics of the associated semigroup generated by degenerate parabolic equations in terms of their global and exponential attractors as well as studying fractal dimension Cited by: 7.

In this paper, we construct a robust family of exponential attractors for a parabolic–hyperbolic phase-field system (PHPFS), which describes phase separation in material sciences, e.g., melting and solidification.

A consequence of this is the existence of finite fractal dimensional global attractors which are both upper and lower semicontinuous at the parameter Cited by: 1. In this paper we consider one-dimensional two-phase Stefan problems for a class of parabolic equations with nonlinear heat source terms and with nonlinear flux conditions on the fixed boundary.

Here, both time-dependent and time-independent source terms and boundary conditions are treated. We investigate the large time behavior of solutions to our problems by using the theory for dynamical. Abstract We prove the existence, some absorbing properties and some regularities of [formula omitted], global attractor for the m-Laplacian type quasilinear parabolic equation in R N Cited by: 6.

We construct global bounded solutions, "non-autonomous equilibria", connections between the trivial solution these "non-autonomous equilibria" and characterize the $\alpha$-limit and $\omega$-limit set of global bounded solutions.

As a consequence, we show that the global attractor of the associated skew-product flow has a gradient : Rita de Cássia D. S. Broche, Alexandre N. Carvalho, José Valero.This paper is a study of global attractors of abstract semilinear parabolic equations and their embeddings in finite-dimensional manifolds.

As is well known, a sufficient condition for the existence of smooth (at least -smooth) finite-dimensional inertial manifolds containing a global attractor is the so-called spectral gap condition for the corresponding linear operator.This paper is addressed to study long-time behavior of fourth order parabolic equations with a critical exponent on unbounded domain R^n.

We show that there exists a compact global attractor in H^2.