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Excerpt from Discontinuous Initial Value Problems and Asymptotic Expansion of Steady-State Solutions
Discontinuous solutions of hyperbolic partial differential equations have often been treated in the mathematical literature. The earlier treat ments dealt mainly with second order equations (see e.g. [l], Recently R. Courant and p.d. Lax[3] extended the theory to first order linear hyper bolic systems and proved an existence theorem for discontinuous solutions of initial value problems. In Part I of this paper we generalize the theory of Courant and Lax in two respects. First we consider more general equations. This generalization is not without interest for it permits the inclusion of some important equations of mathematical physics:$ Second we consider initial boundary value problems rather than pure initial value problems.
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Discontinuous Initial Value Problems and Asymptotic Expansion of SteadyState Solutions Classic Reprint
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781332088478
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Discontinuous Initial Value Problems and Asymptotic Expansion of SteadyState Solutions Classic Reprint
Da: PBShop.store UK, Fairford, GLOS, Regno Unito
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9781332088478
Quantità: 15 disponibili
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Discontinuous Initial Value Problems and Asymptotic Expansion of Steady-State
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Paperback. Condizione: New. Print on Demand. This book presents an extension to the theory of discontinuous initial value problems for symmetric hyperbolic linear differential equations, an area previously studied by Courant and Lax. The author generalizes their theory in two respects. First, the author considers more general equations. This generalization is of interest as it allows the inclusion of equations of mathematical physics. Second, the book considers initial boundary value problems rather than pure initial value problems. This has applications to physical problems as it models problems with both time dependence and spatial dependence. The unique existence theorem for weak solutions of such problems is obtained under conditions which allow the coefficient matrices to have multiple eigenvalues. The author provides an analysis of the discontinuities and a reduction to known theorems for problems with smooth initial data. Following on from this, the book presents an asymptotic expansion of solutions of symmetric hyperbolic linear differential equations and proves the asymptotic nature of the formal expansion. Overall, this book advances the theory of discontinuous solutions of hyperbolic partial differential equations, providing a valuable resource for researchers and students in the field. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781332088478_0
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