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The Action Principle and Partial Differential Equations. (AM-146), Volume 146 (Paperback) Loot Price: R2,198
Discovery Miles 21 980
You Save: R186 (8%)
The Action Principle and Partial Differential Equations. (AM-146), Volume 146 (Paperback): Demetrios Christodoulou

The Action Principle and Partial Differential Equations. (AM-146), Volume 146 (Paperback)

Demetrios Christodoulou

Series: Annals of Mathematics Studies

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List price R2,384 Loot Price R2,198 Discovery Miles 21 980 | Repayment Terms: R206 pm x 12* You Save R186 (8%)

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This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media.

General

Imprint: Princeton University Press
Country of origin: United States
Series: Annals of Mathematics Studies
Release date: 2000
First published: 2000
Authors: Demetrios Christodoulou
Dimensions: 254 x 197 x 19mm (L x W x T)
Format: Paperback - Trade
Pages: 328
ISBN-13: 978-0-691-04957-1
Categories: Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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LSN: 0-691-04957-2
Barcode: 9780691049571

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