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The Action Principle and Partial Differential Equations. (AM-146), Volume 146
Af: Demetrios Christodoulou Engelsk Paperback
SPAR
kr 287
The Action Principle and Partial Differential Equations. (AM-146), Volume 146
Af: Demetrios Christodoulou Engelsk Paperback

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.

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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.

Produktdetaljer
Sprog: Engelsk
Sider: 328
ISBN-13: 9780691049571
Indbinding: Paperback
Udgave:
ISBN-10: 0691049572
Udg. Dato: 17 jan 2000
Længde: 19mm
Bredde: 158mm
Højde: 234mm
Oplagsdato: 17 jan 2000
Forfatter(e): Demetrios Christodoulou
Forfatter(e) Demetrios Christodoulou


Kategori Differentialregning & ligninger


Sprog Engelsk


Indbinding Paperback


Sider 328


Udgave


Længde 19mm


Bredde 158mm


Højde 234mm

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