## Boundary Value Problems for Linear Evolution Partial Differential Equations: Proceedings of the NATO Advanced Study Institute held in Liège, Belgium, September 6–17, 1976Most of the problems posed by Physics to Mathematical Analysis are boundary value problems for partial differential equations and systems. Among them, the problems concerning linear evolution equations have an outstanding position in the study of the physical world, namely in fluid dynamics, elastodynamics, electromagnetism, plasma physics and so on. This Institute was devoted to these problems. It developed essentially the new methods inspired by Functional Analysis and specially by the theories of Hilbert spaces, distributions and ultradistributions. The lectures brought a detailed exposition of the novelties in this field by world known specialists. We held the Institute at the Sart Tilman Campus of the University of Liege from September 6 to 17, 1976. It was attended by 99 participants, 79 from NATO Countries [Belgium (30), Canada (2), Denmark (I), France (15), West Germany (9), Italy (5), Turkey (3), USA (14)] and 20 from non NATO Countries [Algeria (2), Australia (3), Austria (I), Finland (1), Iran (3), Ireland (I), Japan (6), Poland (1), Sweden (I), Zair (1)]. There were 5 courses of_ 6_ h. ollI'. s~. 1. nL lJ. , h. t;l. l. I. rl"~, 1. n,L ,_ h. t;l. l. I. r. !'~ , ?_ n. f~ ?_ h,, |

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### Contents

LAPLACE TRANSFORM METHODS FOR EVOLUTION EQUATIONS | 1 |

I | 27 |

ULTRADISTRIBUTIONS AND HYPERBOLICITY | 157 |

SOME ASPECTS OF THE THEORY OF LINEAR EVOLUTION EQUATIONS | 175 |

SOME TYPICAL FREE BOUNDARY PROBLEMS | 239 |

CRITERIA OF NYPERPOLICITY FOR CONSTANT COEFFICIENT POLYNOMIALS | 313 |

STABILITY OF MOTION FOR SEMILINEAR EQUATIONS | 319 |

THE APPROXIMATION OF SEMIGROUPS OF LINEAR OPERATORS AND THE FINITE ELEMENT METHOD | 351 |

PROPAGATION OF SINGULARITIES FOR HYPERBOLIC MIXED PROBLEMS | 363 |

SPECTRAL AND ASYMPTOTIC ANALYSIS OF ACOUSTIC WAVE PROPAGATION | 385 |

### Other editions - View all

Boundary Value Problems for Linear Evolution Partial Differential Equations ... H.G. Garnir No preview available - 2011 |

### Common terms and phrases

acoustic analysis appear apply assume asymptotic Banach space boundary conditions boundary value problems bounded Cauchy characteristic classical coefficients compact complete cone consider constant construct contains continuous convergence corresponding defined definition denote dependence derivatives described differential equations distribution domain eigenfunctions energy equivalent estimates example exists expansion extended finite fluid follows formula Fourier function given gives Hence holds homogeneous hyperbolic implies inequality initial integral Lemma linear Math matrix method mixed problems Moreover norm normal obtain operator parabolic particular plane polynomial positive proof propagation properties prove reflected relation Remark respect roots satisfies sense shown singular solution space spectral stable sufficiently Suppose surface theorem theory tion transform unique Univ variable verifies wave wave equation wave front zero