3 edition of **Huygens" principle and hyperbolic equations** found in the catalog.

- 299 Want to read
- 3 Currently reading

Published
**1988**
by Academic Press in Boston
.

Written in English

- Wave motion, Theory of.,
- Huygens" principle.,
- Differential equations, Hyperbolic.

**Edition Notes**

Statement | Paul Günther. |

Series | Perspectives in mathematics -- vol. 5 |

Classifications | |
---|---|

LC Classifications | QA927 |

The Physical Object | |

Pagination | lvii, 847 p. ; |

Number of Pages | 847 |

ID Numbers | |

Open Library | OL21122082M |

ISBN 10 | 0123073308 |

• Hyperbolic equations and the wave equation 2. Lecture Two: Solutions to PDEs with boundary conditions and initial conditions • D’Alembert’s solution to the 1D wave equation • Solution to the n-dimensional wave equation • Huygens principle • Energy and uniqueness of solutions 3. Lecture Three: Inhomogeneous solutions - source Cited by: 2. Hyperbolic Partial Differential Equations (Courant Lecture Notes) Peter D. Lax The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity.

We consider a deformed wave equation where the Laplacian operator has been replaced by a differential-difference operator. We prove that this equation does not satisfy Huygens’ principle. Our approach is based on the representation theory of the Lie algebra s l (2, R).Author: Salem Ben Saïd, Sara al-Blooshi, Maryam al-Kaabi, Aisha al-Mehrzi, Fatima al-Saeedi. Basic notions Finite speed of propagation of signals Hyperbolic equations with constant coefficients Hyperbolic equations with variable coefficients Pseudodifferential operators and energy inequalities Existence of solutions Waves and rays Finite difference approximation to hyperbolic equations Scattering theory Hyperbolic systems of conservation laws Huygens' principle for the wave equation 5/5(2).

Huygens’ principle and Dirac-Weyl equation Saverio Pascazio,1,2 Francesco V. Pepe,3,2 and Juan Manuel P erez-Pardo4 1Dipartimento di Fisica and MECENAS, Universit a di Bari, I Bari, Italy 2INFN, Sezione di Bari, I Bari, Italy 3Museo Storico della Fisica e Centro Studi e Ricerche \Enrico Fermi", I Roma, Italy 4Universidad Carlos III de Madrid, Madrid, SpainCited by: 1. A rigorous mathematical formulation of Huygens' principle was first given by H. Helmholtz () and by G. Kirchhoff () for the stationary and non-stationary cases, respectively. The results of J. Hadamard, according to which the solution of the Cauchy problem for the second-order linear hyperbolic equation (*).

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Huygens' Principle and Hyperbolic Equations (Perspectives in Mathematics) by Paul Gunther (Author) ISBN ISBN Why is ISBN important. ISBN.

This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by: Huygens' Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times.

The book aims to present special nontrivial Huygens' operators and to describe their individual properties and to characterize these examples of Huygens' operators within certain more or less comprehensive classes of general hyperbolic Book Edition: 1. Huygens Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved space-times.

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Huygens' Principle and Hyperbolic Equations is devoted to certain mathematical aspects of wave propagation in curved book aims to present special nontrivial Huygens' operators and to describe their individual properties and to characterize these examples of Huygens' operators within certain more or less comprehensive classes of general hyperbolic.

Huygens' Principle and Hyperbolic Equations | Guenther, P. | download | B–OK. Download books for free. Find books. Finite difference approximation to hyperbolic equations 92 92; Scattering theory ; Hyperbolic systems of conservation laws ; Appendix A.

Huygens’ principle for the wave equation on odd-dimensional spheres ; Appendix B. Hyperbolic polynomials ; Appendix C. The multiplicity of eigenvalues Proposition The method using spherical wavefronts from the eikonal equation of the hyperbolic system implies Huygens’ method.

In the case of a steady state solution (see solution u 0(x) of ()) these two methods are equivalent i.e., eikonal equation method of a hyperbolic system and Huygens’ method are equivalent.

Remark File Size: KB. FERMAT’S AND HUYGENS’ PRINCIPLES Proposition For χ given by (), deduce equations () from the Euler equa-tions (). This means Fermat’s method implies the wavefront construction by eikonal equation method of the hyperbolic system.

Proposition The method using spherical wavefronts from the eikonal equation of. Φ(x;y) to a hyperbolic diﬀerential operator L = L(x,∂ x) is contained in the surface of the light-conoid associated to the principal part of L.

See [19, 13] We shall refer, henceforth, to operators satisfying Huygens’ principle in its strict form as operators of Huygens’ type or say they satisfy Huygens’ principle.

An example. The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity.

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