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Regularity of the One-phase Free Boundaries

Posted By: AvaxGenius
Regularity of the One-phase Free Boundaries

Regularity of the One-phase Free Boundaries by Bozhidar Velichkov
English | PDF,EPUB | 2023 | 249 Pages | ISBN : 3031132378 | 20.7 MB

This book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regularity theory and is still an object of intensive research.

Plane Waves and Spherical Means: Applied to Partial Differential Equations

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Plane Waves and Spherical Means: Applied to Partial Differential Equations

Plane Waves and Spherical Means: Applied to Partial Differential Equations by Fritz John
English | PDF | 1981 | 174 Pages | ISBN : 0387905650 | 32.4 MB

The author would like to acknowledge his obligation to all his (;Olleagues and friends at the Institute of Mathematical Sciences of New York University for their stimulation and criticism which have contributed to the writing of this tract. The author also wishes to thank Aughtum S. Howard for permission to include results from her unpublished dissertation, Larkin Joyner for drawing the figures, Interscience Publishers for their cooperation and support, and particularly Lipman Bers, who suggested the publication in its present form.

Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

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Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients

Partial Differential Equations II: Elements of the Modern Theory. Equations with Constant Coefficients by Yu. V. Egorov, M. A. Shubin
English | PDF | 1994 | 269 Pages | ISBN : 3540520015 | 33.1 MB

This book, the first printing of which was published as Volume 31 of the Encyclopaedia of Mathematical Sciences, contains a survey of the modern theory of general linear partial differential equations and a detailed review of equations with constant coefficients. Readers will be interested in an introduction to microlocal analysis and its applications including singular integral operators, pseudodifferential operators, Fourier integral operators and wavefronts, a survey of the most important results about the mixed problem for hyperbolic equations, a review of asymptotic methods including short wave asymptotics, the Maslov canonical operator and spectral asymptotics, a detailed description of the applications of distribution theory to partial differential equations with constant coefficients including numerous interesting special topics.

Numerical Solution of Partial Differential Equations in Science and Engineering

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Numerical Solution of Partial Differential Equations in Science and Engineering

Numerical Solution of Partial Differential Equations in Science and Engineering by Leon Lapidus, George F. Pinder
English | PDF | 1999 | 690 Pages | ISBN : 0471098663 | 23.4 MB

From the reviews of Numerical Solution of Partial Differential Equations in Science and Engineering:
"The book by Lapidus and Pinder is a very comprehensive, even exhaustive, survey of the subject . . . [It] is unique in that it covers equally finite difference and finite element methods."
Burrelle's

Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion

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Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion

Introductory Applications of Partial Differential Equations: With Emphasis on Wave Propagation and Diffusion by G. L. Lamb Jr.
English | PDF | 1995 | 482 Pages | ISBN : 0471311235 | 17.5 MB

This is the ideal text for students and professionals who have some familiarity with partial differential equations, and who now wish to consolidate and expand their knowledge. Unlike most other texts on this topic, it interweaves prior knowledge of mathematics and physics, especially heat conduction and wave motion, into a presentation that demonstrates their interdependence. The result is a superb teaching text that reinforces the reader's understanding of both mathematics and physics. Rather than presenting the mathematics in isolation and out of context, problems in this text are framed to show how partial differential equations can be used to obtain specific information about the physical system being analyzed.

An Introduction to Partial Differential Equations

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An Introduction to Partial Differential Equations

An Introduction to Partial Differential Equations by Daniel J. Arrigo
English | PDF(True) | 2017 | 169 Pages | ISBN : 1681732564 | 1.7 MB

This book is an introduction to methods for solving partial differential equations (PDEs). After the introduction of the main four PDEs that could be considered the cornerstone of Applied Mathematics, the reader is introduced to a variety of PDEs that come from a variety of fields in the Natural Sciences and Engineering and is a springboard into this wonderful subject. The chapters include the following topics: First-order PDEs, Second-order PDEs, Fourier Series, Separation of Variables, and the Fourier Transform. The reader is guided through these chapters where techniques for solving first- and second-order PDEs are introduced. Each chapter ends with a series of exercises illustrating the material presented in each chapter.

Fractional Behaviours Modelling: Analysis and Application of Several Unusual Tools

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Fractional Behaviours Modelling: Analysis and Application of Several Unusual Tools

Fractional Behaviours Modelling: Analysis and Application of Several Unusual Tools by Jocelyn Sabatier, Christophe Farges, Vincent Tartaglione
English | EPUB | 2022 | 139 Pages | ISBN : 3030967484 | 15.2 MB

This book is dedicated to the analysis and modelling of fractional behaviours that mainly result from physical stochastic phenomena (diffusion, adsorption or aggregation, etc.) of a population (ions, molecules, people, etc.) in a constrained environment and that can be found in numerous areas. It breaks with the usual approaches based on fractional models since it proposes to use unusual models which have the advantage of overcoming some of the limitations of fractional models.

Calculus of Variations and Partial Differential Equations (Repost)

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Calculus of Variations and Partial Differential Equations (Repost)

Calculus of Variations and Partial Differential Equations: Topics on Geometrical Evolution Problems and Degree Theory by Luigi Ambrosio
English | PDF | 2000 | 347 Pages | ISBN : 3540648038 | 27.7 MB

The link between Calculus of Variations and Partial Differential Equations has always been strong, because variational problems produce, via their Euler-Lagrange equation, a differential equation and, conversely, a differential equation can often be studied by variational methods. At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on a classical topic (the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to pde's resp.).

Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers

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Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers

Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers by David A. Kopriva
English | PDF | 2009 | 403 Pages | ISBN : 9048122600 | 4.9 MB

This book offers a systematic and self-contained approach to solve partial differential equations numerically using single and multidomain spectral methods. It contains detailed algorithms in pseudocode for the application of spectral approximations to both one and two dimensional PDEs of mathematical physics describing potentials, transport, and wave propagation. David Kopriva, a well-known researcher in the field with extensive practical experience, shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries. The book addresses computational and applications scientists, as it emphasizes the practical derivation and implementation of spectral methods over abstract mathematics.

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations (Repost)

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Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations (Repost)

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by Tarek Poonithara Abraham Mathew
English | PDF | 2008 | 774 Pages | ISBN : 3540772057 | 5.8 MB

Domain decomposition methods are divide and conquer methods for the parallel and computational solution of partial differential equations of elliptic or parabolic type. They include iterative algorithms for solving the discretized equations, techniques for non-matching grid discretizations and techniques for heterogeneous approximations.

Numerical Solution of Partial Differential Equations on Parallel Computers (Repost)

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Numerical Solution of Partial Differential Equations on Parallel Computers (Repost)

Numerical Solution of Partial Differential Equations on Parallel Computers by Are Magnus Bruaset
English | PDF | 2006 | 491 Pages | ISBN : 3540290761 | 7.2 MB

Since the dawn of computing, the quest for a better understanding of Nature has been a driving force for technological development. Groundbreaking achievements by great scientists have paved the way from the abacus to the supercomputing power of today. When trying to replicate Nature in the computer’s silicon test tube, there is need for precise and computable process descriptions. The scienti?c ?elds of Ma- ematics and Physics provide a powerful vehicle for such descriptions in terms of Partial Differential Equations (PDEs).

Loewy Decomposition of Linear Differential Equations

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Loewy Decomposition of Linear Differential Equations

Loewy Decomposition of Linear Differential Equations by Fritz Schwarz
English | PDF | 2012 | 238 Pages | ISBN : 3709112850 | 2.1 MB

The central subject of the book is the generalization of Loewy's decomposition - originally introduced by him for linear ordinary differential equations - to linear partial differential equations. Equations for a single function in two independent variables of order two or three are comprehensively discussed. A complete list of possible solution types is given. Various ad hoc results available in the literature are obtained algorithmically. The border of decidability for generating a Loewy decomposition are explicitly stated. The methods applied may be generalized in an obvious way to equations of higher order, in more variables or systems of such equations.

Hamiltonian Dynamical Systems and Applications (Repost)

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Hamiltonian Dynamical Systems and Applications (Repost)

Hamiltonian Dynamical Systems and Applications by Walter Craig
English | PDF | 2008 | 450 Pages | ISBN : 1402069626 | 6.8 MB

Physical laws are for the most part expressed in terms of differential equations, and natural classes of these are in the form of conservation laws or of problems of the calculus of variations for an action functional.

Spectral Methods in Surface Superconductivity (Repost)

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Spectral Methods in Surface Superconductivity (Repost)

Spectral Methods in Surface Superconductivity by Søren Fournais
English | PDF | 2010 | 332 Pages | ISBN : 0817647961 | 3 MB

During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa.

Nonlinear Partial Differential Equations: Asymptotic Behavior of Solutions and Self-Similar Solutions

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Nonlinear Partial Differential Equations: Asymptotic Behavior of Solutions and Self-Similar Solutions

Nonlinear Partial Differential Equations: Asymptotic Behavior of Solutions and Self-Similar Solutions by Mi-Ho Giga
English | PDF | 2010 | 307 Pages | ISBN : 0817641734 | 2.9 MB

The main focus of this textbook, in two parts, is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. The exposition moves systematically from the basic to more sophisticated concepts with recent developments and several open problems. With challenging exercises, examples, and illustrations to help explain the rigorous analytic basis for the Navier–-Stokes equations, mean curvature flow equations, and other important equations describing real phenomena, this book is written for graduate students and researchers, not only in mathematics but also in other disciplines.