Author : Flavia Smarrazzo
Publisher : Walter de Gruyter GmbH & Co KG
Page : 456 pages
File Size : 10,53 MB
Release : 2022-04-19
Category : Mathematics
ISBN : 3110556901
This carefully written text on measure theory with applications to partial differential equations covers general measure theory, Lebesgue spaces of real-valued and vector-valued functions, different notions of measurability for the latter, weak convergence of functions and measures, Radon and Young measures, capacity, and finally applications to quasilinear parabolic problems (in particular, forward-backward equations).
Author : Baoxiang Wang
Publisher : World Scientific
Page : 298 pages
File Size : 28,40 MB
Release : 2011-08-10
Category : Mathematics
ISBN : 9814458392
This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger equations, nonlinear Klein-Gordon equations, KdV equations as well as Navier-Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.
Author : Wilfried Grecksch
Publisher : De Gruyter Akademie Forschung
Page : 188 pages
File Size : 22,69 MB
Release : 1995
Category : Mathematics
ISBN :
The authors give a self-contained exposition of the theory of stochastic evolution equations. Elements of infinite dimensional analysis, martingale theory in Hilbert spaces, stochastic integrals, stochastic convolutions are applied. Existence and uniqueness theorems for stochastic evolution equations in Hilbert spaces in the sense of the semigroup theory, the theory of evolution operators, and monotonous operators in rigged Hilbert spaces are discussed. Relationships between the different concepts are demonstrated. The results are used to concrete stochastic partial differential equations like parabolic and hyperbolic Ito equations and random constitutive equations of elastic viscoplastic materials. Furthermore, stochastic evolution equations in rigged Hilbert spaces are approximated by time discretization methods.
Author : N. U. Ahmed
Publisher : Springer Nature
Page : 236 pages
File Size : 50,34 MB
Release : 2023-09-12
Category : Mathematics
ISBN : 3031372603
This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach. The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature. This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.
Author : Wolfgang Arendt
Publisher : Birkhäuser
Page : 803 pages
File Size : 37,97 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3034879245
Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
Author : Sandra Carillo
Publisher : Springer Science & Business Media
Page : 247 pages
File Size : 49,15 MB
Release : 2012-12-06
Category : Science
ISBN : 3642840396
Nonlinear Evolution Equations and Dynamical Systems (NEEDS) provides a presentation of the state of the art. Except for a few review papers, the 40 contributions are intentially brief to give only the gist of the methods, proofs, etc. including references to the relevant litera- ture. This gives a handy overview of current research activities. Hence, the book should be equally useful to the senior resercher as well as the colleague just entering the field. Keypoints treated are: i) integrable systems in multidimensions and associated phenomenology ("dromions"); ii) criteria and tests of integrability (e.g., Painlev test); iii) new developments related to the scattering transform; iv) algebraic approaches to integrable systems and Hamiltonian theory (e.g., connections with Young-Baxter equations and Kac-Moody algebras); v) new developments in mappings and cellular automata, vi) applications to general relativity, condensed matter physics, and oceanography.
Author : C.M. Dafermos
Publisher : Elsevier
Page : 609 pages
File Size : 50,23 MB
Release : 2008-10-06
Category : Mathematics
ISBN : 0080931979
The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts
Author : William K. Allard
Publisher : American Mathematical Soc.
Page : 482 pages
File Size : 11,86 MB
Release : 1986
Category : Mathematics
ISBN : 0821814702
Includes twenty-six papers that survey a cross section of work in modern geometric measure theory and its applications in the calculus of variations. This title provides an access to the material, including introductions and summaries of many of the authors' much longer works and a section containing 80 open problems in the field.
Author : Klaus Ecker
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 39,51 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 0817682104
* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow. * Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.
Author : J. Malek
Publisher : CRC Press
Page : 334 pages
File Size : 31,79 MB
Release : 2019-08-16
Category : Mathematics
ISBN : 1000723127
This book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering.
