7 edition of **Variational methods for discontinuous structures** found in the catalog.

- 82 Want to read
- 21 Currently reading

Published
**1996** by Birkhäuser in Basel, Boston .

Written in English

- Calculus of variations -- Congresses.,
- Differential equations, Partial -- Congresses.

**Edition Notes**

Statement | Raul Serapioni, Franco Tomarelli, editors. |

Series | Progress in nonlinear differential equations and their applications ;, v. 25 |

Contributions | Serapioni, Raul, 1951-, Tomarelli, Franco, 1955- |

Classifications | |
---|---|

LC Classifications | QA315 .V365 1996 |

The Physical Object | |

Pagination | viii, 192 p. : |

Number of Pages | 192 |

ID Numbers | |

Open Library | OL997257M |

ISBN 10 | 0817652736, 3764352736 |

LC Control Number | 96035953 |

ment of such methods. The so-called \structure-preserving methods" are one strong branch of them (see, for example, Hairer{Lubich{Wanner [9]). In thispaper, along the lineof these studies, weareparticularly interested in certain variational structures of PDEs and their associated conservation and dissipation properties. The basic problem of the calculus of variations is to determine the function u(x) that extremizes a functional F==\[Integral]_SubscriptBox[x^StyleBox[min, FontSlant -> Italic], SubscriptBox[x, StyleBox[max, FontSlant -> Italic]]]f[u(x),u^\[Prime](x),x]\[DifferentialD]x. In general, there can be more than one independent variable and the integrand f can depend on several functions and . In the above, u(x, t) with is the structural displacement vector, σ is the symmetric Cauchy stress tensor, and (x,t) with is the scalar acoustic velocity potential. The phase velocity of acoustic wave propagation is denoted by c; ρ s > 0 and ρ f > 0 are the reference densities of the structure and fluid, respectively. A superposed dot indicates partial differentiation with respect to time t. familiar with variational methods (at the level of Bolza's problem) can obtain a knowledge of the discontinuous problem with a minimum time expendi- ture. All of the above papers are rather formidable and leave much of the developmental work to the reader. The notation used in Hunt's work will be retained, with the exception.

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