Symmetrization and stabilization of solutions of nonlinear elliptic equations /
Saved in:
| Author / Creator: | Efendiev, Messoud, author. |
|---|---|
| Imprint: | Cham, Switzerland : Springer, [2018] |
| Description: | 1 online resource |
| Language: | English |
| Series: | Fields Institute monographs, 2194-3079 ; volume 36 Fields Institute monographs ; 36. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11718403 |
MARC
| LEADER | 00000cam a2200000Ii 4500 | ||
|---|---|---|---|
| 001 | 11718403 | ||
| 005 | 20210625184500.5 | ||
| 006 | m o d | ||
| 007 | cr cnu|||unuuu | ||
| 008 | 181022s2018 sz ob 000 0 eng d | ||
| 015 | |a GBB8J9542 |2 bnb | ||
| 016 | 7 | |a 019098414 |2 Uk | |
| 019 | |a 1057853994 |a 1059302493 |a 1081277083 |a 1086551693 |a 1088969936 |a 1103257606 | ||
| 020 | |a 9783319984070 |q (electronic bk.) | ||
| 020 | |a 3319984071 |q (electronic bk.) | ||
| 020 | |a 9783319984087 |q (print) | ||
| 020 | |a 331998408X | ||
| 020 | |a 9783030074913 |q (print) | ||
| 020 | |a 3030074919 | ||
| 020 | |z 9783319984063 | ||
| 020 | |z 3319984063 | ||
| 024 | 7 | |a 10.1007/978-3-319-98407-0 |2 doi | |
| 035 | |a (OCoLC)1057471976 |z (OCoLC)1057853994 |z (OCoLC)1059302493 |z (OCoLC)1081277083 |z (OCoLC)1086551693 |z (OCoLC)1088969936 |z (OCoLC)1103257606 | ||
| 035 | 9 | |a (OCLCCM-CC)1057471976 | |
| 037 | |a com.springer.onix.9783319984070 |b Springer Nature | ||
| 040 | |a N$T |b eng |e rda |e pn |c N$T |d N$T |d YDX |d EBLCP |d GW5XE |d UAB |d STF |d OCLCF |d UKMGB |d VT2 |d CAUOI |d LEAUB |d MERER |d FIE |d UKAHL |d OCLCQ | ||
| 049 | |a MAIN | ||
| 050 | 4 | |a QA377 | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 072 | 7 | |a PBKJ |2 bicssc | |
| 072 | 7 | |a PBKJ |2 thema | |
| 100 | 1 | |a Efendiev, Messoud, |e author. |0 http://id.loc.gov/authorities/names/n2003008293 | |
| 245 | 1 | 0 | |a Symmetrization and stabilization of solutions of nonlinear elliptic equations / |c Messoud Efendiev. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c [2018] | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Fields Institute monographs, |x 2194-3079 ; |v volume 36 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | |a Online resource; title from PDF title page (EBSCO, viewed October 23, 2018). | ||
| 505 | 0 | |a Intro; Preface; Contents; 1 Preliminaries; 1.1 Functional Spaces and Their Properties; 1.1.1 Lp Spaces; 1.1.2 Sobolev Spaces; 1.2 Linear Elliptic Boundary Value Problems; 1.3 Nemytskii Operator; 1.4 Maximum Principles and Their Applications; 1.4.1 Classical Maximum Principles; 1.5 Uniform Estimates and Boundedness of the Solutions of Semilinear Elliptic Equations; 1.6 The Sweeping Principle and the Moving Plane Method in a Bounded Domain; 1.7 The Sliding and the Moving Plane Method in General Domains; 1.8 Variational Solutions of Elliptic Equations | |
| 505 | 8 | |a 1.9 Elliptic Regularity for the Neumann Problem for the Laplace Operator on an Infinite Edge2 Trajectory Dynamical Systems and Their Attractors; 2.1 Kolmogorov epsilon-Entropy and Its Asymptotics in FunctionalSpaces; 2.2 Global Attractors and Finite-Dimensional Reduction; 2.3 Classification of Positive Solutions of Semilinear Elliptic Equations in a Rectangle: Two Dimensional Case; 2.3.1 Sketch of the Proof of Theorem 2.4; 2.4 Existence of Solutions of Nonlinear Elliptic Systems; 2.5 Regularity of Solutions; 2.6 Boundedness of Solutions as; 2.7 Basic Definitions: Trajectory Attractor | |
| 505 | 8 | |a 2.8 Trajectory Attractor of Nonlinear Elliptic System2.9 Dependence of the Trajectory Attractor on the UnderlyingDomain; 2.10 Regularity of Attractor; 2.11 Trajectory Attractor of an Elliptic Equation with a Nonlinearity That Depends on x; 2.12 Examples of Trajectory Attractors; 2.13 The Trajectory Dynamical Approach for the Nonlinear Elliptic Systems in Non-smooth Domains; 2.13.1 Existence of Solutions; 2.13.2 Trajectory Attractor for the Nonlinear Elliptic System; 2.13.3 Stabilization of Solutions in the Potential Case; 2.13.4 Regular and Singular Part of the Trajectory Attractor | |
| 505 | 8 | |a 2.14 The Dynamics of Fast Nonautonomous Travelling Waves and Homogenization3 Symmetry and Attractors: The Case N<=3; 3.1 Introduction; 3.2 A Priori Estimates and Solvability Results; 3.3 The Attractor; 3.4 Symmetry and Stabilization; 4 Symmetry and Attractors: The Case N<=4; 4.1 Introduction; 4.2 A Priori Estimates and Solvability Results; 4.3 The Attractor; 4.4 Symmetry and Stabilization; 5 Symmetry and Attractors; 5.1 Introduction; 5.1.1 Statement of Results; 5.2 The Dynamical System Approach; 5.3 Proof of Theorem 5.1; 5.4 Proof of Theorem 5.2; 5.4.1 Symmetry of the Profiles | |
| 505 | 8 | |a 5.4.2 Completion of the Proof of Theorem 5.25.5 Proof of Theorem 5.3; 5.5.1 Positivity of Solutions; 5.5.2 Completion of the Proof of Theorem 5.3; 6 Symmetry and Attractors: Arbitrary Dimension; 6.1 Introduction; 6.2 The PDE Approach; 6.2.1 Problem in the Quarter-Space; 6.2.2 Problem in the Half-Space; 6.3 Classification Results in the Whole Space RN or in the Half-Space RN-1x(0,+infty) with Dirichlet BoundaryConditions; 6.4 The Dynamical Systems' Approach; 7 The Case of p-Laplacian Operator; 7.1 Introduction; 7.2 Some Basic Results; 7.2.1 The Weak Sweeping Principle | |
| 520 | |a This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists. | ||
| 650 | 0 | |a Differential equations, Elliptic. |0 http://id.loc.gov/authorities/subjects/sh85037895 | |
| 650 | 0 | |a Differential equations, Nonlinear. |0 http://id.loc.gov/authorities/subjects/sh85037906 | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Nonlinear science. |2 bicssc | |
| 650 | 7 | |a Differential calculus & equations. |2 bicssc | |
| 650 | 7 | |a Differential equations, Elliptic. |2 fast |0 (OCoLC)fst00893458 | |
| 650 | 7 | |a Differential equations, Nonlinear. |2 fast |0 (OCoLC)fst00893474 | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Print version: |a Efendiev, Messoud. |t Symmetrization and stabilization of solutions of nonlinear elliptic equations. |d Cham, Switzerland : Springer, [2018] |z 3319984063 |z 9783319984063 |w (OCoLC)1043842815 |
| 830 | 0 | |a Fields Institute monographs ; |v 36. |0 http://id.loc.gov/authorities/names/n93094774 | |
| 903 | |a HeVa | ||
| 929 | |a oclccm | ||
| 999 | f | f | |i 2006196f-83b5-56cc-937d-ad4e1ce31570 |s 72992fce-5000-523c-b6c0-d218ee3bc3c8 |
| 928 | |t Library of Congress classification |a QA377 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-3-319-98407-0 |z Springer Nature |g ebooks |i 12557976 | ||