Cauchy's Problem for Hyperbolic Equations
| Author | : Lars Gårding |
| Publisher | : |
| Total Pages | : 322 |
| Release | : 1958 |
| Genre | : Cauchy problem |
| ISBN | : |
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Cauchys Problem For Hyperbolic Equations PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Cauchys Problem For Hyperbolic Equations PDF full book. Access full book title Cauchys Problem For Hyperbolic Equations.
Lectures on Cauchy's Problem in Linear Partial Differential Equations
| Author | : Jacques Hadamard |
| Publisher | : |
| Total Pages | : 336 |
| Release | : 1923 |
| Genre | : Cauchy problem |
| ISBN | : |
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On the Cauchy Problem
| Author | : Sigeru Mizohata |
| Publisher | : Academic Press |
| Total Pages | : 186 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 148326906X |
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Notes and Reports in Mathematics in Science and Engineering, Volume 3: On the Cauchy Problem focuses on the processes, methodologies, and mathematical approaches to Cauchy problems. The publication first elaborates on evolution equations, Lax-Mizohata theorem, and Cauchy problems in Gevrey class. Discussions focus on fundamental proposition, proof of theorem 4, Gevrey property in t of solutions, basic facts on pseudo-differential, and proof of theorem 3. The book then takes a look at micro-local analysis in Gevrey class, including proof and consequences of theorem 1. The manuscript examines Schrödinger type equations, as well as general view-points on evolution equations. Numerical representations and analyses are provided in the explanation of these type of equations. The book is a valuable reference for mathematicians and researchers interested in the Cauchy problem.
The Cauchy Problem for Hyperbolic Operators
| Author | : Karen Yagdjian |
| Publisher | : De Gruyter Akademie Forschung |
| Total Pages | : 408 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : |
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Cauchy's Problem for Hyperbolic Equations
| Author | : Lars Gårding |
| Publisher | : |
| Total Pages | : 302 |
| Release | : 1958 |
| Genre | : Differential equations, Partial |
| ISBN | : |
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New Trends in the Theory of Hyperbolic Equations
| Author | : Michael Reissig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 520 |
| Release | : 2006-03-21 |
| Genre | : Mathematics |
| ISBN | : 3764373865 |
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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.
The Hyperbolic Cauchy Problem
| Author | : Kunihiko Kajitani |
| Publisher | : Springer |
| Total Pages | : 175 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 354046655X |
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The approach to the Cauchy problem taken here by the authors is based on theuse of Fourier integral operators with a complex-valued phase function, which is a time function chosen suitably according to the geometry of the multiple characteristics. The correctness of the Cauchy problem in the Gevrey classes for operators with hyperbolic principal part is shown in the first part. In the second part, the correctness of the Cauchy problem for effectively hyperbolic operators is proved with a precise estimate of the loss of derivatives. This method can be applied to other (non) hyperbolic problems. The text is based on a course of lectures given for graduate students but will be of interest to researchers interested in hyperbolic partial differential equations. In the latter part the reader is expected to be familiar with some theory of pseudo-differential operators.
Partial Differential Equations in Classical Mathematical Physics
| Author | : Isaak Rubinstein |
| Publisher | : Cambridge University Press |
| Total Pages | : 704 |
| Release | : 1998-04-28 |
| Genre | : Mathematics |
| ISBN | : 9780521558464 |
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The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.
Hyperbolic Partial Differential Equations
| Author | : Serge Alinhac |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 159 |
| Release | : 2009-06-17 |
| Genre | : Mathematics |
| ISBN | : 0387878238 |
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This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the self-contained chapters, as well as references at the end of the book, enable ease-of-use for both the student and the independent researcher.
Hyperbolic Systems with Analytic Coefficients
| Author | : Tatsuo Nishitani |
| Publisher | : Springer |
| Total Pages | : 245 |
| Release | : 2013-11-19 |
| Genre | : Mathematics |
| ISBN | : 3319022733 |
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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.
