Parabolic Boundary Value Problems (Practical Engineering Perspectives, #101) (Operator Theory: Advances and Applications, #101)
by Samuil D. Eidelman
This monograph is devoted to the theory of general parabolic bondary problems. It starts with basic notions and various illustrative examples, followed by a detailed and systematic exposition of the L2-theory of parabolic boundary value problems with smooth functions and distributions of arbitrary finite order. A survey of the Cauchy problem and boundary value problem in spaces of smooth functions broadens the scope of the work. Special attention is paid to detailed study of examples illustratin...
Yes, this is another Calculus book. However, it fits in a niche between the two predominant types of such texts. It could be used as a textbook, albeit a streamlined one — it contains exposition on each topic, with an introduction, rationale, train of thought, and solved examples with accompanying suggested exercises. It could be used as a solution guide — because it contains full written solutions to each of the hundreds of exercises posed inside. But its best position is right in between thes...
Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium
This book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.
The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker-Planck equation, the Feymann-Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the...
This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.
Formal And Analytic Solutions Of Differential Equations
The book provides the reader with an overview of the actual state of research in ordinary and partial differential equations in the complex domain. Topics include summability and asymptotic study of both ordinary and partial differential equations, and also q-difference and differential-difference equations. This book will be of interest to researchers and students who wish to expand their knowledge of these fields.With the latest results and research developments and contributions from experts...
Lattice Gas Methods for Partial Differential Equations (Santa Fe Methods for Partial Differential Equations, #4)
by Gary D. Doolen, Muriel Frisch, Brosl Hasslacher, Steven Orszag, Stephen Wolfram, and Santa Fe Instit
Degenerate Diffusions (The IMA Volumes in Mathematics and its Applications, #47)
This IMA Volume in Mathematics and its Applications DEGENERATE DIFFUSIONS is based on the proceedings of a workshop which was an integral part of the 1990- 91 IMA program on "Phase Transitions and Free Boundaries". The aim of this workshop was to provide some focus in the study of degenerate diffusion equations, and by involving scientists and engineers as well as mathematicians, to keep this focus firmly linked to concrete problems. We thank Wei-Ming Ni, L.A. Peletier and J.L. Vazquez for organ...
The Navier-Stokes Equations (Modern Birkhauser Classics) (Birkhauser Advanced Texts / Basler Lehrbucher)
by Hermann Sohr
The primary objective of this monograph is to develop an elementary and se- containedapproachtothemathematicaltheoryofaviscousincompressible?uid n in a domain ? of the Euclidean spaceR , described by the equations of Navier- Stokes. The book is mainly directed to students familiar with basic functional analytic tools in Hilbert and Banach spaces. However, for readers' convenience, in the ?rst two chapters we collect, without proof some fundamental properties of Sobolev spaces, distributions, ope...
Partial Differential Equations: Advances in Spectral and High Order Methods
Designed for the junior- and senior-level course in Partial Differential Equations, this new edition builds upon the solid strengths of the previous editions and has been revised to provide a more patient development of the core concepts. The material has been divided into three parts covering preliminary material, basic concepts, and advanced topics. Parts One and Two have also been reorganized and refined to provide more complete examples to help students master the content. The Sturm-Louivill...
A Treatise on the Calculus of Finite Differences (Cambridge Library Collection - Mathematics)
by George Boole
Self-taught mathematician and father of Boolean algebra, George Boole (1815-1864) published A Treatise on the Calculus of Finite Differences in 1860 as a sequel to his Treatise on Differential Equations (1859). Both books became instant classics that were used as textbooks for many years and eventually became the basis for our contemporary digital computer systems. The book discusses direct theories of finite differences and integration, linear equations, variations of a constant, and equations...
2018 Planner Weekly and Monthly (Weekly Planner Calendar 2018, #1)
by Evan Mica
This text on domain decomposition focuses on the notion that by breaking the domain of the original problem into subdomains, such an approach can, if properly implemented, lead to considerable speedup. the methods are suited for parallel computers.
This book is a collection of lecture notes for the LIASFMA Shanghai Summer School on 'One-dimensional Hyperbolic Conservation Laws and Their Applications' which was held during August 16 to August 27, 2015 at Shanghai Jiao Tong University, Shanghai, China. This summer school is one of the activities promoted by Sino-French International Associate Laboratory in Applied Mathematics (LIASFMA in short). LIASFMA was established jointly by eight institutions in China and France in 2014, which is aimed...
Affine Bernstein Problems And Monge-ampere Equations
by An-Min Li, Fang Jia, Udo Simon, and Ruiwei Xu
In this monograph, the interplay between geometry and partial differential equations (PDEs) is of particular interest. It gives a selfcontained introduction to research in the last decade concerning global problems in the theory of submanifolds, leading to some types of Monge-Ampere equations.From the methodical point of view, it introduces the solution of certain Monge-Ampere equations via geometric modeling techniques. Here geometric modeling means the appropriate choice of a normalization and...
Nonlinear Theory of Pseudodifferential Equations on a Half-Line (North-Holland Mathematics Studies, #194)
by Nakao Hayashi and Elena Kaikina
This book is the first attempt to develop systematically a general theory of the initial-boundary value problems for nonlinear evolution equations with pseudodifferential operators Ku on a half-line or on a segment. We study traditionally important problems, such as local and global existence of solutions and their properties, in particular much attention is drawn to the asymptotic behavior of solutions for large time. Up to now the theory of nonlinear initial-boundary value problems with a gene...
Since the first edition of this book the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In this revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus o...
Nonlinear Partial Differential Equations And Applications: Proceedings Of The Conference
Contents: Direct and Inverse Diffraction by Periodic Structures (G Bao); Weak Flow of H -Systems (Y-M Chen); Strongly Compact Attractor for Dissipative Zakharov Equations (B-L Guo et al.); C Oex -Solutions of Generalized Porous Medium Equations (M otani & Y Sugiyama); Cauchy Problem for Generalized IMBq Equation (G-W Chen & S-B Wang); Inertial Manifolds for a Nonlocal KuramotoOCoSivashinsky Equation (J-Q Duan et al.); Weak Solutions of the Generalized Magnetic Flow Equations (S-H He & Z-D Dai);...
In this memoir we consider the Dirichlet problem for parabolic operators in a half space with singular drift terms. In chapter I we begin the study of a parabolic PDE modeled on the pullback of the heat equation in certain time varying domains considered by Lewis-Murray and Hofmann-Lewis. In chapter II we obtain mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the $L^q(R^n)$ Dirichlet problem for these PDE's has a solution when...