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Concentration Analysis and Applications to PDE by Adimurthi,K. Sandeep,Ian Schindler,Cyril Tintarev Pdf
Concentration analysis provides, in settings without a priori available compactness, a manageable structural description for the functional sequences intended to approximate solutions of partial differential equations. Since the introduction of concentration compactness in the 1980s, concentration analysis today is formalized on the functional-analytic level as well as in terms of wavelets, extends to a wide range of spaces, involves much larger class of invariances than the original Euclidean rescalings and has a broad scope of applications to PDE. This book represents current research in concentration and blow-up phenomena from various perspectives, with a variety of applications to elliptic and evolution PDEs, as well as a systematic functional-analytic background for concentration phenomena, presented by profile decompositions based on wavelet theory and cocompact imbeddings.
Moving Boundary PDE Analysis by William Schiesser Pdf
Mathematical models stated as systems of partial differential equations (PDEs) are broadly used in biology, chemistry, physics and medicine (physiology). These models describe the spatial and temporial variations of the problem system dependent variables, such as temperature, chemical and biochemical concentrations and cell densities, as a function of space and time (spatiotemporal distributions). For a complete PDE model, initial conditions (ICs) specifying how the problem system starts and boundary conditions (BCs) specifying how the system is defined at its spatial boundaries, must also be included for a well-posed PDE model. In this book, PDE models are considered for which the physical boundaries move with time. For example, as a tumor grows, its boundary moves outward. In atherosclerosis, the plaque formation on the arterial wall moves inward, thereby restricting blood flow with serious consequences such as stroke and myocardial infarction (heart attack). These two examples are considered as applications of the reported moving boundary PDE (MBPDE) numerical method (algorithm). The method is programmed in a set of documented routines coded in R, a quality, open-source scientific programming system. The routines are provided as a download so that the reader/analyst/researcher can use MFPDE models without having to first study numerical methods and computer programming.
Partial Differential Equations by Walter A. Strauss Pdf
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Concentration Compactness by Kyril Tintarev,Karl-Heinz Fieseler Pdf
Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades. This unique volume fulfills the need for a source book that usefully combines a concise formulation of the method, a range of important applications to variational problems, and background material concerning manifolds, non-compact transformation groups and functional spaces. Highlighting the role in functional analysis of invariance and, in particular, of non-compact transformation groups, the book uses the same building blocks, such as partitions of domain and partitions of range, relative to transformation groups, in the proofs of energy inequalities and in the weak convergence lemmas.
Analysis and Geometry by Ali Baklouti,Aziz El Kacimi,Sadok Kallel,Nordine Mir Pdf
This book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the field of several complex variables, who passed away in 2011. All research articles were written by leading experts, some of whom are prize winners in the fields of complex geometry, algebraic geometry and analysis. The book offers a valuable resource for all researchers interested in recent developments in analysis and geometry.
Partial Differential Equations by Michael Shearer,Rachel Levy Pdf
An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors
Linear Partial Differential Equations and Fourier Theory by Marcus Pivato Pdf
This highly visual introductory textbook provides a rigorous mathematical foundation for all solution methods and reinforces ties to physical motivation.
Differential Equation Analysis in Biomedical Science and Engineering by William E. Schiesser Pdf
Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general PDE computation through various biomedical science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.
Numerical PDE Analysis of Retinal Neovascularization by William E. Schiesser Pdf
Numerical PDE Analysis of Retinal Neovascularization Mathematical Model Computer Implementation in R provides a methodology for the analysis of neovascularization (formation of blood capillaries) in the retina. It describes the starting point—a system of three partial differential equations (PDEs)—that define the evolution of (1) capillary tip density, (2) blood capillary density and (3) concentration of vascular endothelial growth factor (VEGF) in the retina as a function of space (distance along the retina), x, and time, t, the three PDE dependent variables for (1), (2) and (3), and designated as u1(x, t), u2(x, t), u3(x, t), amongst other topics. Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms Authored by a leading researcher and educator in PDE models
Partial Differential Equations in Mechanics 1 by A.P.S. Selvadurai Pdf
This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Partial Differential Equation Analysis in Biomedical Engineering by W. E. Schiesser Pdf
Gives graduate students and researchers an introductory overview of partial differential equation analysis of biomedical engineering systems through detailed examples.
Numerical Analysis Using R by Graham W. Griffiths Pdf
This book presents the latest numerical solutions to initial value problems and boundary valu problems described by ODES (Ordinary differencial equations) and PDEs (partiral differential equations). The primary focus in numerical solutions to initial value problems (IVPs) and boundary value problems (BVPs).
Binding and Dissociation Kinetics for Different Biosensor Applications Using Fractals by Ajit Sadana Pdf
The application of biosensors is expanding in different areas. These are portable and convenient devices that permit the rapid, accurate, and reliable detection of analytes of interest present either in the atmosphere or in aqueous or in liquid phases. The detection of glucose levels in blood for the effective management of diabetes is one. Though different biosensors have been designed for an increasing number of applications, the kinetics of binding (and dissociation) of analytes by the receptors on the biosensor surfaces has not been given enough attention in the open literature. This is a very important area of investigation since it significantly impacts biosensor performance parameters such as stability, sensitivity, selectivity, response time, regenerability, etc. Binding and Dissociation Kinetics for Different Biosensor Applications Using Fractals addresses this critical need besides helping to correct or demonstrate the need to modify the present software available with commercial biosensors that determines the kinetics of analyte-receptor reactions on biosensor surfaces. * first book to provide detailed kinetic analysis of the binding and dissociation reactions that are occuring on the biosensor surface * addresses the area of analyte-receptor binding and dissociation kinetics occurring on biosensor surfaces * provides physical insights into reactions occuring on biosensor surfaces
