New tools for nonlinear PDEs and application /

New tools for nonlinear PDEs and application /

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Bibliographic Details
Imprint:Cham, Switzerland : Birkhäuser, [2019]
Description:1 online resource
Language:English
Series:Trends in mathematics, 2297-024X
Trends in mathematics.
Subject:
Differential equations, Partial.
Differential equations, Nonlinear.
Differential equations, Nonlinear.
Differential equations, Partial.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11895248
Hidden Bibliographic Details
Varying Form of Title:New tools for nonlinear partial differential equations and application
Other authors / contributors:D'Abbicco, Marcello, editor.
Ebert, Marcelo Rempel, editor.
Georgiev, Vladimir, editor.
Ozawa, Tohru, editor.
ISBN:9783030109370
3030109372
9783030109363
Notes:Includes bibliographical references.
Online resource; title from PDF title page (EBSCO, viewed May 9, 2019).
Summary:This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.
Table of Contents:
  • Intro; Preface; Contents; On Effective PDEs of Quantum Physics; 1 Introduction; 2 Hartree and Gross-Pitaevski Equations; 2.1 Origin and Properties; 2.1.1 Properties of the Hartree and Gross-Pitaevski Equations; 2.2 Particles Coupled to the Electromagnetic Field; 3 The (Generalized) Hartree-Fock Equations; 3.1 Formulation and Properties; 3.1.1 Exchange Energy Term; 3.2 Static gHF Equations; 3.3 Coupling to the Electromagnetic Field; 3.4 Static gHFem Equations; 3.4.1 Free Energy; 3.4.2 Electrostatics; 4 Density Functional Theory; 4.1 Crystals; 4.2 Macroscopic Perturbations
  • 5 Hartree-Fock-Bogoliubov Equations6 Bogoliubov-de Gennes Equations; 6.1 Formulation; 6.2 Symmetries; 6.3 Conservation Laws; 6.4 Stationary Bogoliubov-de Gennes Equations; 6.5 Free Energy; 6.6 Ground/Gibbs States; 6.7 Symmetry Breaking; 6.8 Stability; 6.8.1 Normal States; 6.8.2 Superconducting States; 6.8.3 Mixed States; 6.8.4 Magnetic Flux Quantization; 7 Existence of Periodic Solutions by the Variational Technique; References; Critical Exponents for Differential Inequalities with Riemann-Liouville and Caputo Fractional Derivatives; 1 Introduction; 1.1 Notation; 2 Global Weak Solutions
  • 3 A Suitable Test Function4 Proof of Theorem 1; 5 Proof of Theorem 2; 6 Decay Estimates for the Fractional Subdiffusive Equation; 6.1 Proof of Lemma 3; 6.2 Decay Estimates; 6.3 Proof of Theorems 3 and 4; References; Weakly Coupled Systems of Semilinear Effectively Damped Waves with Different Time-Dependent Coefficients in the Dissipation Terms and Different Power Nonlinearities; 1 Introduction; 1.1 Notations; 2 Main Results; 2.1 Low Regular Data; 2.2 Data from Energy Space; 2.3 Data from Sobolev Spaces with Suitable Regularity; 2.4 Large Regular Data; 3 Philosophy of Our Approach
  • 3.1 Proof of Theorem 2.13.2 Proof of Theorem 2.6; 3.3 Proof of Theorem 2.8; 3.4 Proof of Theorem 2.11; 4 Concluding Remarks; Appendix; References; Incompressible Limits for Generalisations to Symmetrisable Systems; 1 Introduction; 1.1 An Example: The Incompressible Limit for the Euler System; 1.2 An Example: The Quasineutral Limit for the Euler-Poisson System; 2 Assumptions and Main Results; 3 The Uniform Existence Interval; 4 The Incompressible Limit; 5 An Application; 6 Concluding Remarks; References; The Critical Exponent for Evolution Models with Power Non-linearity; 1 Introduction

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