New tools for nonlinear PDEs and application. ([2019])

• Record Type: Book
• Further Information: Note: Editors, Marcello D'Abbicco, Marcelo Rempel Ebert, Vladimir Georgiev and Tohru Ozawa.
• Editors: D'Abbicco, Marcello; Ebert, Marcelo Rempel; Georgiev, Vladimir; Ozawa, Tohru
• 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
• Publisher Details: Cham, Switzerland : Birkhäuser
• Publication Date: 2019
• Extent: 1 online resource
• Subjects: 515.353; Differential equations, Partial; Differential equations, Nonlinear; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030109370; 3030109372
• Related ISBNs: 9783030109363
• Notes: Note: Includes bibliographical references.; Note: Online resource; title from PDF title page (EBSCO, viewed May 9, 2019).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.