Vector Valued Partial Differential Equations And Applications

Author : Bernard Dacorogna
Publisher : Springer
ISBN 13 : 3319545140
Total Pages : 250 pages
Book Rating : 4.41/5 ( download)

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Download or read book Vector-Valued Partial Differential Equations and Applications written by Bernard Dacorogna and published by Springer. This book was released on 2017-05-29 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

Author : Wolfgang Arendt
Publisher : Springer Science & Business Media
ISBN 13 : 3034850751
Total Pages : 526 pages
Book Rating : 4.59/5 ( download)

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Download or read book Vector-valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>. ) = 1 e-). . tu(t) dt of u for large real>. .

Author : Wolfgang Arendt
Publisher : Springer Science & Business Media
ISBN 13 : 3034800878
Total Pages : 540 pages
Book Rating : 4.77/5 ( download)

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Download or read book Vector-valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2011-04-05 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph gives a systematic account of the theory of vector-valued Laplace transforms, ranging from representation theory to Tauberian theorems. In parallel, the theory of linear Cauchy problems and semigroups of operators is developed completely in the spirit of Laplace transforms. Existence and uniqueness, regularity, approximation and above all asymptotic behaviour of solutions are studied. Diverse applications to partial differential equations are given. The book contains an introduction to the Bochner integral and several appendices on background material. It is addressed to students and researchers interested in evolution equations, Laplace and Fourier transforms, and functional analysis. The second edition contains detailed notes on the developments in the last decade. They include, for instance, a new characterization of well-posedness of abstract wave equations in Hilbert space due to M. Crouzeix. Moreover new quantitative results on asymptotic behaviour of Laplace transforms have been added. The references are updated and some errors have been corrected.

Author : Heinrich Begehr
Publisher : Springer Science & Business Media
ISBN 13 : 1461332761
Total Pages : 367 pages
Book Rating : 4.63/5 ( download)

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Download or read book Partial Differential and Integral Equations written by Heinrich Begehr and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of the Proceedings of the congress ISAAC '97 collects the con tributions of the four sections 1. Function theoretic and functional analytic methods for pde, 2. Applications of function theory of several complex variables to pde, 3. Integral equations and boundary value problems, 4. Partial differential equations. Most but not all of the authors have participated in the congress. Unfortunately some from Eastern Europe and Asia have not managed to come because of lack of financial support. Nevertheless their manuscripts of the proposed talks are included in this volume. The majority of the papers deal with complex methods. Among them boundary value problems in particular the Riemann-Hilbert, the Riemann (Hilbert) and related problems are treated. Boundary behaviour of vector-valued functions are studied too. The Riemann-Hilbert problem is solved for elliptic complex equations, for mixed complex equations, and for several complex variables. It is considered in a general topological setting for mappings into q;n and related to Toeplitz operators. Convolution operators are investigated for nilpotent Lie groups leading to some consequences for the null space of the tangential Cauchy Riemann operator. Some boundary value problems for overdetermined systems in balls of q;n are solved explicitly. A survey is given for the Gauss-Manin connection associated with deformations of curve singularities. Several papers deal with generalizations of analytic functions with various applications to mathematical physics. Singular integrals in quaternionic anal ysis are studied which are applied to the time-harmonic Maxwell equations.

Author : Suzanne Lenhart
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110792788
Total Pages : 365 pages
Book Rating : 4.82/5 ( download)

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Download or read book Potentials and Partial Differential Equations written by Suzanne Lenhart and published by Walter de Gruyter GmbH & Co KG. This book was released on 2023-05-22 with total page 365 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to the legacy of David R. Adams (1941-2021) and discusses calculus of variations, functional - harmonic - potential analysis, partial differential equations, and their applications in modeling, mathematical physics, and differential - integral geometry.

Author : Wolfgang Arendt
Publisher : Springer Science & Business Media
ISBN 13 : 9783764365493
Total Pages : 544 pages
Book Rating : 4.98/5 ( download)

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Download or read book Vector-Valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by Springer Science & Business Media. This book was released on 2001 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear evolution equations in Banach spaces have seen important developments in the last two decades. This is due to the many different applications in the theory of partial differential equations, probability theory, mathematical physics, and other areas, and also to the development of new techniques. One important technique is given by the Laplace transform. It played an important role in the early development of semigroup theory, as can be seen in the pioneering monograph by Rille and Phillips [HP57]. But many new results and concepts have come from Laplace transform techniques in the last 15 years. In contrast to the classical theory, one particular feature of this method is that functions with values in a Banach space have to be considered. The aim of this book is to present the theory of linear evolution equations in a systematic way by using the methods of vector-valued Laplace transforms. It is simple to describe the basic idea relating these two subjects. Let A be a closed linear operator on a Banach space X. The Cauchy problern defined by A is the initial value problern (t 2 0), (CP) {u'(t) = Au(t) u(O) = x, where x E X is a given initial value. If u is an exponentially bounded, continuous function, then we may consider the Laplace transform 00 u(>.) = 1 e- ). . tu(t) dt of u for large real>.

Author : Joseph Grifone
Publisher : World Scientific
ISBN 13 : 9814495360
Total Pages : 228 pages
Book Rating : 4.63/5 ( download)

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Download or read book Variational Principles for Second-Order Differential Equations written by Joseph Grifone and published by World Scientific. This book was released on 2000-05-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler–Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi–Civita for some Riemann metric. To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer–Quillen–Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc. Contents:An Introduction to Formal Integrability Theory of Partial Differential SystemsFrölicher–Nijenhuis Theory of DerivationsDifferential Algebraic Formalism of ConnectionsNecessary Conditions for Variational SpraysObstructions to the Integrability of the Euler–Lagrange SystemThe Classification of Locally Variational Sprays on Two-Dimensional ManifoldsEuler–Lagrange Systems in the Isotropic Case Readership: Mathematicians. Keywords:Calculus of Variations;Inverse Problem;Euler-Lagrange Equation;Sprays;Formal Integrability;Involution;Janet-Riquier Theory;Spencer TheoryReviews: “Everybody seriously interested in the modern theory of the inverse problem of the calculus of variations should take a look at this book.” Zentralblatt MATH

Author : E. C. Zachmanoglou
Publisher : Courier Corporation
ISBN 13 : 048613217X
Total Pages : 432 pages
Book Rating : 4.74/5 ( download)

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Download or read book Introduction to Partial Differential Equations with Applications written by E. C. Zachmanoglou and published by Courier Corporation. This book was released on 2012-04-20 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Author : Wolfgang Arendt
Publisher :
ISBN 13 : 9783034800884
Total Pages : 554 pages
Book Rating : 4.86/5 ( download)

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Download or read book Vector-Valued Laplace Transforms and Cauchy Problems written by Wolfgang Arendt and published by . This book was released on 2011-04-07 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
ISBN 13 : 0821868896
Total Pages : 545 pages
Book Rating : 4.98/5 ( download)

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Download or read book Partial Differential Equations and Boundary-Value Problems with Applications written by Mark A. Pinsky and published by American Mathematical Soc.. This book was released on 2011 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.