Series: Operator Theory: Advances and Applications, Vol. 216
1st Edition., 2011, 400 p., Hardcover
ISBN: 978-3-0348-0068-6
Due: April 29, 2011
About this book
The book provides a quick overview of a wide range of active research areas in partial differential equations. The book can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions from authors from a large variety of countries on different aspects of partial differential equations, such as evolution equations and estimates for their solutions, control theory, inverse problems, nonlinear equations, elliptic theory on singular domains, numerical approaches.
Content Level ā Research
Keywords ā Evolution equations - control theory - inverse problems - nonlinear equations
Related subjects ā Analysis - Dynamical Systems & Differential Equations
Series: Progress in Nonlinear Differential Equations and Their Applications, Vol. 80
1st Edition., 2011, X, 680 p., Hardcover
ISBN: 978-3-0348-0074-7
Due: May 2, 2011
The volume originates from the 'Conference on Nonlinear Parabolic Problems' held in celebration of Herbert Amann 70th birthday at the Banach Center in Bedlewo, Poland. It features a collection of peer-reviewed research papers by recognized experts highlighting recent advances in fields of Herbert Amann's intererest such as nonlinear evolution equations, fluid dynamics, quasi-linear parabolic equations and systems, functional analysis, and more.
Content Level ā Research
Keywords ā Nonlinear evolution equations - Partial differential equations - fluid dynamics - functional analysis
Related subjects ā Dynamical Systems & Differential Equations
Series: Stochastic Modelling and Applied Probability, Vol. 65
1st Edition., 2011, X, 340 p., Hardcover
ISBN: 978-3-642-16535-1
Due: September 12, 2011
The L_2-theory of parabolic SPDEs is presented in this book. The development
of the theory of SPDEs is motivated by problems arising in practice surrounding
the numerical calculations of nonlinear filters for partially observed
diffusion processes. To address these questions, the dependence of SPDEs
on the driving semimartingales is investigated and new results on their
numerical approximations are also given. In contrast to previous expositions,
SPDEs driven by random measures and discontinuous semimartingales are also
considered, and the theory of SPDEs driven by Levy processes are included
as special cases.
The author introduces a more general theory of SPDEs developing the theory of stochastic evolution equations in Banach spaces. He presents applications to large classes of linear and nonlinear SPDEs and , in particular, he developes a theory of SPDEs with unbounded coefficients in weighted Sobolev spaces.
In this unique book regularity properties of the solutions are obtained via new results on dependence of the solutions on parameters, and existence and uniqueness theorems for parabolic SPDEs on smooth domains of R^d are proven. Furthermore, the present book makes the theory more accessible for beginners, because initial linear parabolic SPDEs on the whole R^d are considered, and the main existence and uniqueness results are obtained by elementary methods while exercises and applications are also provided
Content Level ā Research
Keywords ā 60H15, 35R60 - ItoLs Formula in Banach Spaces - Nonlinear Filtering - Stochastic Evolution Equations - Stochastic PDEs
Related subjects ā Dynamical Systems & Differential Equations - Probability Theory and Stochastic Processes
Series: Applied Mathematical Sciences, Vol. 92
2011, X, 290 p. 43 illus., Hardcover
ISBN: 978-1-4419-7837-0
Due: January 25, 2012
Mathematically rigorous treatment of special relativity with precise statement of the physical interpretation
Detailed introduction to the theory of spinors in Minkowski spacetime
Thorough treatments of numerous topics not generally discussed at the introductory level
This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeemanfs characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Diracfs famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. The treatment presumes only a knowledge of linear algebra and, in two appendices, elementary point-set topology.
Content Level ā Graduate
Keywords ā Minkowski spacetime - Penrose theorem - theory of spinors
Related subjects ā Geometry & Topology - Theoretical, Mathematical & Computational Physics