The Action Principle and Partial Differential Equations is popular PDF and ePub book, written by Demetrios Christodoulou in 2000-01-17, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Action Principle and Partial Differential Equations can be Read Online from any device for your convenience.
The Action Principle and Partial Differential Equations Book PDF Summary
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.
Detail Book of The Action Principle and Partial Differential Equations PDF
- Author : Demetrios Christodoulou
- Release : 17 January 2000
- Publisher : Princeton University Press
- ISBN : 0691049572
- Genre : Mathematics
- Total Page : 332 pages
- Language : English
- PDF File Size : 20,8 Mb
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