Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations
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Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations
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Author : Maria Colombo
language : en
Publisher: Springer
Release Date : 2017-06-07
Flows Of Non Smooth Vector Fields And Degenerate Elliptic Equations written by Maria Colombo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-07 with Mathematics categories.
The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.
Weighted Sobolev Spaces And Degenerate Elliptic Equations
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Author : Albo Carlos Cavalheiro
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2023-09-29
Weighted Sobolev Spaces And Degenerate Elliptic Equations written by Albo Carlos Cavalheiro and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-29 with Mathematics categories.
In various applications, we can meet boundary value problems for elliptic equations whose ellipticity is disturbed in the sense that some degeneration or singularity appears. This bad behavior can be caused by the coefficients of the corresponding differential operator as well as by the solution itself. There are several very concrete problems in various practices which lead to such differential equations, such as glaciology, non-Newtonian fluid mechanics, flows through porous media, differential geometry, celestial mechanics, climatology, and reaction-diffusion problems, among others. This book is based on research by the author on degenerate elliptic equations. This book will be a useful reference source for graduate students and researchers interested in differential equations.
Spaces Of Measures And Their Applications To Structured Population Models
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Author : Christian Düll
language : en
Publisher: Cambridge University Press
Release Date : 2021-10-07
Spaces Of Measures And Their Applications To Structured Population Models written by Christian Düll and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-07 with Mathematics categories.
Presents a comprehensive analytical framework for structured population models in spaces of Radon measures and their numerical approximation.
An Introduction To The Geometrical Analysis Of Vector Fields With Applications To Maximum Principles And Lie Groups
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Author : Stefano Biagi
language : en
Publisher: World Scientific
Release Date : 2018-12-05
An Introduction To The Geometrical Analysis Of Vector Fields With Applications To Maximum Principles And Lie Groups written by Stefano Biagi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-05 with Mathematics categories.
This book provides the reader with a gentle path through the multifaceted theory of vector fields, starting from the definitions and the basic properties of vector fields and flows, and ending with some of their countless applications, in the framework of what is nowadays called Geometrical Analysis. Once the background material is established, the applications mainly deal with the following meaningful settings:
Transmission Problems For Elliptic Second Order Equations In Non Smooth Domains
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Author : Mikhail Borsuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-02
Transmission Problems For Elliptic Second Order Equations In Non Smooth Domains written by Mikhail Borsuk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-02 with Mathematics categories.
This book investigates the behaviour of weak solutions to the elliptic transmisssion problem in a neighborhood of boundary singularities: angular and conic points or edges, considering this problem both for linear and quasi-linear equations.
Fokker Planck Kolmogorov Equations
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Author : Vladimir I. Bogachev
language : en
Publisher: American Mathematical Society
Release Date : 2022-02-10
Fokker Planck Kolmogorov Equations written by Vladimir I. Bogachev and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-10 with Mathematics categories.
This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker–Planck–Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.
Smooth Ergodic Theory Of Random Dynamical Systems
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Author : Pei-Dong Liu
language : en
Publisher: Springer
Release Date : 2006-11-14
Smooth Ergodic Theory Of Random Dynamical Systems written by Pei-Dong Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
This book studies ergodic-theoretic aspects of random dynam- ical systems, i.e. of deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems, and can be viewed as an update of Kifer's book. An entropy formula of Pesin's type occupies the central part. The introduction of relation numbers (ch.2) is original and most methods involved in the book are canonical in dynamical systems or measure theory. The book is intended for people interested in noise-perturbed dynam- ical systems, and can pave the way to further study of the subject. Reasonable knowledge of differential geometry, measure theory, ergodic theory, dynamical systems and preferably random processes is assumed.
On First And Second Order Planar Elliptic Equations With Degeneracies
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Author : Abdelhamid Meziani
language : en
Publisher:
Release Date : 2011
On First And Second Order Planar Elliptic Equations With Degeneracies written by Abdelhamid Meziani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Degenerate differential equations categories.
This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.
On The Geometry Of Diffusion Operators And Stochastic Flows
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Author : K.D. Elworthy
language : en
Publisher: Springer
Release Date : 2007-01-05
On The Geometry Of Diffusion Operators And Stochastic Flows written by K.D. Elworthy and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.
Stochastic differential equations, and Hoermander form representations of diffusion operators, can determine a linear connection associated to the underlying (sub)-Riemannian structure. This is systematically described, together with its invariants, and then exploited to discuss qualitative properties of stochastic flows, and analysis on path spaces of compact manifolds with diffusion measures. This should be useful to stochastic analysts, especially those with interests in stochastic flows, infinite dimensional analysis, or geometric analysis, and also to researchers in sub-Riemannian geometry. A basic background in differential geometry is assumed, but the construction of the connections is very direct and itself gives an intuitive and concrete introduction. Knowledge of stochastic analysis is also assumed for later chapters.
Rohlin Flows On Von Neumann Algebras
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Author : Toshihiko Masuda
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-10-05
Rohlin Flows On Von Neumann Algebras written by Toshihiko Masuda and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with Conjugacy classes categories.
The authors will classify Rohlin flows on von Neumann algebras up to strong cocycle conjugacy. This result provides alternative approaches to some preceding results such as Kawahigashi's classification of flows on the injective type II1 factor, the classification of injective type III factors due to Connes, Krieger and Haagerup and the non-fullness of type III0 factors. Several concrete examples are also studied.