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Variable Lebesgue Spaces And Hyperbolic Systems
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Book Synopsis Variable Lebesgue Spaces and Hyperbolic Systems by : David Cruz-Uribe
Download or read book Variable Lebesgue Spaces and Hyperbolic Systems written by David Cruz-Uribe and published by Springer. This book was released on 2014-07-22 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.
Book Synopsis Arithmetic Geometry over Global Function Fields by : Gebhard Böckle
Download or read book Arithmetic Geometry over Global Function Fields written by Gebhard Böckle and published by Springer. This book was released on 2014-11-13 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009-2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell-Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings.
Book Synopsis Some Existence Theorems for Semilinear Hyperbolic Systems in One Space Variable by : Luc C. Tartar
Download or read book Some Existence Theorems for Semilinear Hyperbolic Systems in One Space Variable written by Luc C. Tartar and published by . This book was released on 1980 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study semilinear hyperbolic systems with quadratic nonlinearities which originate in the kinetic theory of gas as a simplification of Boltzmann's equation. Local existence is well known for these equations and the main problem is to prove global existence for nonnegative bounded data. Except for the unrealistic case where a bounded invariant region exists, no result of this type is known in three space dimensions. As in all preceding results, based on the work of Mimura-Nishida and Crandall-Tartar, we restrict ourselves to one space dimension. We show global existence for a quite general class of systems and under some special condition (S) we obtain information on the asymptotic behaviour and on scattering when the data have small L1 norm. The new idea lies in the introduction of some functional spaces where some products can be defined; this enables us to define an appropriate notion of solution in L1 and then use it to obtain local and global existence for data in L1 (R).
Book Synopsis P(x)-bi-laplacian: Application On Time-pdes In Viscoelasticity by : Khaled Zennir
Download or read book P(x)-bi-laplacian: Application On Time-pdes In Viscoelasticity written by Khaled Zennir and published by World Scientific. This book was released on 2024-07-26 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main subject of our book is to use the (p, p(x) and p(x))-bi-Laplacian operator in some partial differential systems, where we developed and obtained many results in quantitative and qualitative point of view.
Book Synopsis New Trends in the Theory of Hyperbolic Equations by : Michael Reissig
Download or read book New Trends in the Theory of Hyperbolic Equations written by Michael Reissig and published by Springer Science & Business Media. This book was released on 2006-03-21 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting several developments in the theory of hyperbolic equations, this book's contributions deal with questions of low regularity, critical growth, ill-posedness, decay estimates for solutions of different non-linear hyperbolic models, and introduce new approaches based on microlocal methods.
Book Synopsis Hyperbolic Systems of Conservation Laws in Several Space Variables by : Peter D. Lax
Download or read book Hyperbolic Systems of Conservation Laws in Several Space Variables written by Peter D. Lax and published by . This book was released on 1985 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hyperbolic Systems with Analytic Coefficients by : Tatsuo Nishitani
Download or read book Hyperbolic Systems with Analytic Coefficients written by Tatsuo Nishitani and published by Springer. This book was released on 2013-11-19 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph focuses on the well-posedness of the Cauchy problem for linear hyperbolic systems with matrix coefficients. Mainly two questions are discussed: (A) Under which conditions on lower order terms is the Cauchy problem well posed? (B) When is the Cauchy problem well posed for any lower order term? For first order two by two systems with two independent variables with real analytic coefficients, we present complete answers for both (A) and (B). For first order systems with real analytic coefficients we prove general necessary conditions for question (B) in terms of minors of the principal symbols. With regard to sufficient conditions for (B), we introduce hyperbolic systems with nondegenerate characteristics, which contain strictly hyperbolic systems, and prove that the Cauchy problem for hyperbolic systems with nondegenerate characteristics is well posed for any lower order term. We also prove that any hyperbolic system which is close to a hyperbolic system with a nondegenerate characteristic of multiple order has a nondegenerate characteristic of the same order nearby.
Book Synopsis Hyperbolic Systems of Conservation Laws in Several Space Variables by : Peter D. Lax
Download or read book Hyperbolic Systems of Conservation Laws in Several Space Variables written by Peter D. Lax and published by . This book was released on 1985 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Approximation of Hyperbolic Systems of Conservation Laws by : Edwige Godlewski
Download or read book Numerical Approximation of Hyperbolic Systems of Conservation Laws written by Edwige Godlewski and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work is devoted to the theory and approximation of nonlinear hyper bolic systems of conservation laws in one or two space variables. It follows directly a previous publication on hyperbolic systems of conservation laws by the same authors, and we shall make frequent references to Godlewski and Raviart (1991) (hereafter noted G. R. ), though the present volume can be read independently. This earlier publication, apart from a first chap ter, especially covered the scalar case. Thus, we shall detail here neither the mathematical theory of multidimensional scalar conservation laws nor their approximation in the one-dimensional case by finite-difference con servative schemes, both of which were treated in G. R. , but we shall mostly consider systems. The theory for systems is in fact much more difficult and not at all completed. This explains why we shall mainly concentrate on some theoretical aspects that are needed in the applications, such as the solution of the Riemann problem, with occasional insights into more sophisticated problems. The present book is divided into six chapters, including an introductory chapter. For the reader's convenience, we shall resume in this Introduction the notions that are necessary for a self-sufficient understanding of this book -the main definitions of hyperbolicity, weak solutions, and entropy present the practical examples that will be thoroughly developed in the following chapters, and recall the main results concerning the scalar case.
Book Synopsis Dynamics Beyond Uniform Hyperbolicity by : Christian Bonatti
Download or read book Dynamics Beyond Uniform Hyperbolicity written by Christian Bonatti and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n
Book Synopsis The Journal of Integral Equations and Applications by :
Download or read book The Journal of Integral Equations and Applications written by and published by . This book was released on 2016 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Moduli of Weighted Hyperplane Arrangements by : Valery Alexeev
Download or read book Moduli of Weighted Hyperplane Arrangements written by Valery Alexeev and published by Birkhäuser. This book was released on 2015-05-18 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families. Concrete examples are developed that take advantage of the intricate interplay between Algebraic Geometry and Combinatorics. Compactifications of moduli spaces play a crucial role in Number Theory, String Theory, and Quantum Field Theory – to mention just a few. In particular, the notion of compactification of moduli spaces has been crucial for solving various open problems and long-standing conjectures. Further, the book reports on compactification techniques for moduli spaces in a large class where computations are possible, namely that of weighted stable hyperplane arrangements (shas).
Book Synopsis Variable Lebesgue Spaces by : David V. Cruz-Uribe
Download or read book Variable Lebesgue Spaces written by David V. Cruz-Uribe and published by Springer Science & Business Media. This book was released on 2013-02-12 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
Book Synopsis Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes) by : Tatsien Li
Download or read book Hyperbolic Problems: Theory, Numerics And Applications (In 2 Volumes) written by Tatsien Li and published by World Scientific. This book was released on 2012-09-28 with total page 793 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume book is devoted to mathematical theory, numerics and applications of hyperbolic problems. Hyperbolic problems have not only a long history but also extremely rich physical background. The development is highly stimulated by their applications to Physics, Biology, and Engineering Sciences; in particular, by the design of effective numerical algorithms. Due to recent rapid development of computers, more and more scientists use hyperbolic partial differential equations and related evolutionary equations as basic tools when proposing new mathematical models of various phenomena and related numerical algorithms.This book contains 80 original research and review papers which are written by leading researchers and promising young scientists, which cover a diverse range of multi-disciplinary topics addressing theoretical, modeling and computational issues arising under the umbrella of ';Hyperbolic Partial Differential Equations';. It is aimed at mathematicians, researchers in applied sciences and graduate students.
Book Synopsis Hyperbolic Equations and Frequency Interactions by : Luis A. Caffarelli
Download or read book Hyperbolic Equations and Frequency Interactions written by Luis A. Caffarelli and published by American Mathematical Soc.. This book was released on with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multi-dimensional Hyperbolic Partial Differential Equations by : Sylvie Benzoni-Gavage
Download or read book Multi-dimensional Hyperbolic Partial Differential Equations written by Sylvie Benzoni-Gavage and published by Oxford University Press, USA. This book was released on 2007 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: Authored by leading scholars, this comprehensive text presents a view of the multi-dimensional hyperbolic partial differential equations, with a particular emphasis on problems in which modern tools of analysis have proved useful. It is useful to graduates and researchers in both hyperbolic PDEs and compressible fluid dynamics.
Book Synopsis New Trends in Analysis and Geometry by : Mohamed A. Khamsi
Download or read book New Trends in Analysis and Geometry written by Mohamed A. Khamsi and published by Cambridge Scholars Publishing. This book was released on 2020-01-24 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique mathematical volume brings together geometers, analysts, differential equations specialists and graph-theorists to provide a glimpse on recent mathematical trends whose commonalities have hitherto remained, for the most part, unnoticed. The applied mathematician will be pleasantly surprised with the interpretation of a voting system in terms of the fixed points of a mapping given in the book, as much as the classical analyst will be enthusiastic to find detailed discussions on the generalization of the notion of metric space, in which the metric takes values on an abstract monoid. Classical themes on fixed point theory are adapted to the diverse setting of graph theory, thus uncovering a set of tools whose power and versatility will be appreciated by mathematicians working on either area. The volume also includes recent results on variable exponent spaces which reveal much-needed connections with partial differential equations, while the incipient field of variational inequalities on manifolds, also explored here, will be of interest to researchers from a variety of fields.
