From particle systems to partial differential equations : International Conference, Particle Systems and PDEs VI, VII and VIII, 2017-2019 / / Cédric Bernardin [and four others] editors

• Pubblicazione: Cham, Switzerland : , : Springer, , [2021]; ©2021
• Descrizione fisica: 1 online resource (400 pages)
• Disciplina: 515.353
• Soggetto topico: Differential equations, Partial; Kinetic theory of matter - Mathematics; Equacions en derivades parcials; Teoria cinètica de la matèria
• Soggetto genere / forma: Congressos; Llibres electrònics
• Persona (resp. second.): BernardinCédric
• Nota di contenuto: Intro -- Preface -- Contents -- Brief Discussion of the Lr-Theory for the Boltzmann Equation: Cutoff and Non-cutoff -- 1 Introduction -- 2 The Cutoff Case -- 2.1 Propagation of the Lr-Norm for the Cutoff Case -- 2.2 Propagation of the Linfty-Norm for the Cutoff Case -- 3 The Non-cutoff Case -- 3.1 The Lr-Theory for the Non-cutoff Case -- 3.2 The Linfty-Theory for the Non-cutoff Case -- References -- The Maxwell-Stefan Diffusion Limit of a Hard-Sphere Kinetic Model for Mixtures -- 1 Introduction -- 2 Kinetic Model -- 3 Scaled Kinetic Equations, Properties and Assumptions -- 3.1 Scaled Kinetic Equations -- 3.2 Properties of the Collision Operators -- 3.3 Assumptions -- 4 The Maxwell-Stefan Diffusion Limit -- 4.1 Continuity Equations for the Species -- 4.2 Momentum Balance Equations for the Species -- 4.3 Formal Asymptotics -- 5 Conclusion -- References -- An Asymptotic Preserving Scheme for a Stochastic Linear Kinetic Equation in the Diffusion Regime -- 1 Introduction -- 2 General Setting -- 3 The Diffusion Limit -- 3.1 The Macroscopic Equation -- 3.2 The Micro-Macro Decomposition -- 3.3 Formal Analytical Limit -- 4 The Numerical Scheme -- 4.1 Construction of the Scheme -- 4.2 Formal Numerical Limit -- 4.3 Stability Results -- 5 Numerical Tests -- 6 Conclusion and Perspectives -- References -- Zero-Range Process in Random Environment -- 1 Introduction -- 2 A Preliminary Illustration: Traffic Jams -- 3 Description of the Model, Basic Properties -- 3.1 The Process and Its Invariant Measures -- 3.2 Assumptions on the Environment, and Consequences -- 4 Convergence -- 4.1 Previous Results for Convergence -- 4.2 Our Results for Convergence -- 5 Hydrodynamics -- 5.1 Previous Results for Hydrodynamic Limit -- 5.2 Our Results on Hydrodynamic Limits -- 5.3 Examples -- 6 Local Equilibrium -- References. ; On Non-equilibrium Fluctuations for the Stirring Process with Births and Deaths -- 1 Introduction -- 2 Preliminaries -- 2.1 The Model -- 2.2 Hydrodynamic Limit -- 2.3 Fluctuations -- 3 Closure of the Martingale -- 4 Macroscopic Limit of the Fluctuation Field -- 4.1 Direct Calculation of the Variance -- 4.2 Continuous Kernel Variance Using Martingales -- References -- On Existence, Uniqueness and Banach Space Regularity for Solutions of Boltzmann Equations Systems for Monatomic Gas Mixtures -- 1 Introduction -- 2 Kinetic Model -- 2.1 Collision Process -- 2.2 The System of Boltzmann Equations -- 2.3 Representations of the Collision Operator -- 3 Moments and Functional Space -- 4 Statement of the Problem -- 5 Angular Averaging Estimate for the Mixture System Gain Operators -- 6 Polynomially and Exponentially Weighted L1 Theory -- 6.1 Polynomially Weighted L1 Norms -- 6.2 Exponentially Weighted L1 Norms -- 7 Existence and Uniqueness Theory -- 8 Polynomial and Exponential Weighted Lp Theory, 1< -- p< -- infty -- 9 Polynomial and Exponential Linfty Theory -- References -- Hydrodynamics of Weakly Asymmetric Exclusion with Slow Boundary -- 1 Introduction -- 2 Statement of Results -- 2.1 The Models -- 2.2 Hydrodynamic Equations -- 2.3 Hydrodynamic Limit -- 3 Heuristics for Hydrodynamic Equations -- 4 Tightness -- 5 Replacement Lemmas -- 5.1 Estimates on Dirichlet Forms -- 5.2 Proof of Lemma 5 -- 5.3 Proof of Lemma 6 -- Appendix -- References -- Recent Developments on the Modelling of Cell Interactions in Autoimmune Diseases -- 1 Introduction -- 2 The Biological Scenario -- 3 The Model for Autoimmune Diseases -- 3.1 The Kinetic Description of the Cellular Interactions -- 3.2 The Macroscopic Equations -- 3.3 The Wellposedeness of the Model -- 3.4 Numerical Solutions of the Model -- 4 The Extended Model with Immunotherapy -- 4.1 The Model. ; 4.2 Mathematical Analysis and Optimal Control -- 4.3 Numerical Solutions of the Model with Immunotherapy -- 5 Conclusion and Future Projects -- References -- Geometrical Structures of the Instantaneous Current and Their Macroscopic Effects: Vortices and Perspectives in Non-gradient Models -- 1 Introduction and Results -- 2 Definitions -- 3 Particle Models and Instantaneous Current -- 3.1 Exclusion Process and the 2-SEP -- 3.2 Instantaneous Current in Particle Systems -- 4 Energy-Mass Models -- 4.1 KMP Model and Generalization, Dual KMP, Gaussian Model -- 4.2 Weakly Asymmetric Energy-Mass Models -- 4.3 Instantaneous Current of Energy-Mass Systems -- 5 Discrete Hodge Decomposition in Interacting Particle Systems -- 5.1 Functional Discrete Hodge Decomposition and Lattice Gases -- 5.2 The One Dimensional Case -- 5.3 The Two Dimensional Case -- 6 Interacting Particle Systems with Vorticity -- 7 Scaling Limits and Transport Coefficients of Diffusive Models -- 7.1 Qualitative Derivation of Hydrodynamics -- 8 Scaling Limit of an Exclusion Process with Vorticity -- 9 Green-Kubo's Formula and Perspectives in Non-gradient Particles Systems -- References -- Porous Medium Model: An Algebraic Perspective and the Fick's Law -- 1 Introduction -- 1.1 Organization of the Paper -- 1.2 The Model -- 2 Fick's Law for the PMM with Slow Reservoirs -- 2.1 Currents -- 2.2 Integrated Currents -- 2.3 Empirical Measures -- 2.4 Fick's Law -- 2.5 Proof of Theorem 1 -- 3 Stochastic Duality Relations for the PMM -- 3.1 Algebraic Approach to Duality -- 3.2 Porous Medium Model Described with the mathfraksu(2) Algebra -- 3.3 Duality Relations for the Porous Medium Model -- References -- Forward Utilities and Mean-Field Games Under Relative Performance Concerns -- 1 Introduction -- 2 Asset Specialization, Forward Utilities and CARA Preferences -- 2.1 Forward Dynamic Utilities (Classic). ; 3 Forward Relative Performance Criteria -- 3.1 Forward Relative Performance Criteria -- 3.2 The Forward Nash Equilibrium -- 4 The Mean Field Game -- 4.1 Agents Through Type-Distribution and the Market -- 4.2 The Equilibrium -- 4.3 Solving the Optimization Problem -- 4.4 Mean-Field Dynamic Model Selection with Large Horizons -- 5 Outlook and Open Questions -- 6 Supplementary Calculations -- References -- The Boundary Driven Zero-Range Process -- 1 Introduction -- 2 Definition of the Model -- 3 Invariant Measure -- 4 Hydrostatic Limit -- 5 Attractiveness -- 6 Tightness -- 6.1 Related Martingales -- 6.2 Proof of Tightness -- 7 Limit Points are Concentrated on Absolutely Continuous Measures -- 8 Hydrodynamic Limit -- 9 Heuristics of the Hydrodynamic Equation -- 10 Heuristics for Hydrodynamics of the General Model -- References -- Partial Regularity in Time for the Landau Equation (with Coulomb Interaction) -- 1 The Landau Equation -- 2 A Notion of Weak Solutions of the Landau Equation -- 2.1 Villani's H-Solutions -- 2.2 Suitable Solutions -- 3 Partial Regularity in t for Suitable Solutions -- 4 Existence Theory for Suitable Solutions -- 4.1 Formal H Theorem -- 4.2 The Desvillettes Theorem -- 4.3 Sketch of the Proof of Proposition 1 -- 5 The 1st De Giorgi Type Lemma -- 6 The Improved De Giorgi Lemma -- 7 Proof of the Partial Regularity Theorem -- 8 Final Remarks and Open Problems -- References -- Recent Developments on the Well-Posedness Theory for Vlasov-Type Equations -- 1 An Introduction to Vlasov-Type Equations in Plasma Physics -- 1.1 The Vlasov-Poisson System: The Electrons' View-Point -- 1.2 The Vlasov-Poisson System with Massless Electrons: The Ions' View-Point -- 2 Well-Posedness for Vlasov Equations with Smooth Interactions -- 3 Well-Posedness for the Vlasov-Poisson System. ; 4 Well-Posedness Theory for the Vlasov-Poisson System with Massless Electrons -- 4.1 Strategy for mathbbTd -- 4.2 Strategy for mathbbR3 -- References -- Charge-Current Correlation Identities for Stochastic Interacting Particle Systems -- 1 Introduction -- 2 Classical Setting and Results -- 2.1 Notation and General Properties of the Interacting Particle System -- 2.2 Some Important Expectation Values and General Properties of the Invariant Measure -- 2.3 Results -- 3 Proofs -- 3.1 Proposition 1 -- 3.2 Theorems 1 and 2 -- 3.3 Theorem 3 -- 4 Comments on Phase Separation and the Decay of Correlations -- References -- From the Hartree to the Vlasov Dynamics: Conditional Strong Convergence -- 1 Introduction -- 2 Preliminary Estimates -- 3 Proof of Theorem 1 -- References -- From the Boltzmann Description for Mixtures to the Maxwell-Stefan Diffusion Equations -- 1 Introduction -- 2 The Maxwell-Stefan Equations -- 3 The Boltzmann System for Monatomic Inert Gaseous Mixtures -- 4 The Boltzmann System for Polyatomic Reactive or Non-reactive Gas Mixtures -- 5 The Maxwell-Stefan Diffusion Limit for Non-reactive Boltzmann Systems -- 5.1 The Formal Asymptotics -- 5.2 The Rigorous Diffusive Asymptotics -- 6 The Maxwell-Stefan Diffusion Limit for Reactive Kinetic Systems -- 7 Some Related Research Directions -- References -- Alternative Quantum Formulations and Systems at the Classical-Quantum Border -- 1 Introduction -- 2 Quantum Mechanics and Deformation Theory -- 3 Quantum Mechanics in the Tomography Approach -- 4 Applications -- 4.1 Kinetic Equations and Quantum Corrections -- 4.2 A Quantum Lyapunov Exponent -- 5 Quantizers and Dequantizers: An Unified View of Alternative Quantum Formulations -- References.
• Titolo autorizzato: From Particle Systems to Partial Differential Equations
• ISBN: 3-030-69784-3
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996466392803316
• Lo trovi qui: Univ. di Salerno
• Serie: Springer proceedings in mathematics & statistics ; ; Volume 352.