Last edited by Kajikora
Wednesday, July 22, 2020 | History

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

Huygens" principle and hyperbolic equations

by Paul GuМ€nther

  • 299 Want to read
  • 3 Currently reading

Published by Academic Press in Boston .
Written in English

    Subjects:
  • Wave motion, Theory of.,
  • Huygens" principle.,
  • Differential equations, Hyperbolic.

  • Edition Notes

    StatementPaul Günther.
    SeriesPerspectives in mathematics -- vol. 5
    Classifications
    LC ClassificationsQA927
    The Physical Object
    Paginationlvii, 847 p. ;
    Number of Pages847
    ID Numbers
    Open LibraryOL21122082M
    ISBN 100123073308

    • 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    We consider a deformed wave equation where the Laplacian operator has been replaced by a differential-difference operator.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 by Paul GuМ€nther Download PDF EPUB FB2

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 operators.

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.

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 operators.

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.

Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and Author: Pavel B. Bochev, Max D. Gunzburger. Genre/Form: Electronic books: Additional Physical Format: Print version: Günther, Paul, Huygens' principle and hyperbolic equations.

Boston: Academic Press, © Huygens' principle and hyperbolic equations. Boston: Academic Press, © (OCoLC) Material Type: Internet resource: Document Type: Book.

Nishiwada, Huygens' principle for a wave equation and the asymptotic behavior of solutions along geodesics, in Hyperbolic equations and related topics (S. Mizohata, ed.), Academic Press, Zentralblatt MATH: Mathematical Reviews (MathSciNet): MRAuthor: Bent Ørsted.

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.

The physical notion of Huygens’Principle goes back to the classical “Traité de la Lumière” by Christian Huygens, published in Various aspects of this fundamental principle in the theory of wave propagation were later discussed in the works of Kirchhof, Poisson, Beltrami and other by: A new class of linear second order hyperbolic partial differential operators satisfying Huygens’ principle in Minkowski spaces is presented.

The construction reveals a direct connection between Huygens’ principle and the theory of solitary wave solutions of the Korteweg-de Vries equation. Fundamental solutions of selected Huygens’ equations are constructed by using a new adaptation of the group theoretic technique for distributions.

It is observed that the hierarchy of Huygens’ equations is closely related to that of rational solutions for higher Korteweg-de Vries by: 3. Fermat's and huygens' principles, and hyperbolic equations and their equivalence in wavefront construction September Neural, Parallel and Scientific Computations 21(3) Günther, P.

Huygens' Principle and Hyperbolic Equations (Academic Press, ) Hörmander, L. Lectures on Nonlinear Hyperbolic Differential Equations (Springer, ; original notes ) A bunch more have appeared in more recent years, some of which have already been mentioned.

According to Huygens’ principle, every point on a wave front traveling at speed v is the origin of a secondary wavelet that also propagates at speed er Figure A, which shows the interface between air and a liquid transparent refractive index of air isso the speed of light in air is very near to its speed in a vacuum.Huygens' principle (HP) is understood as a universal principle governing not only the propagation of light.

According to Hadamard's rigorous definition, HP comprehends the principle of action-by-proximity (cf Faraday's field theory etc) and the superposition of secondary wavelets (Huygens' construction).Author: Peter Enders.Huygens' principle following from the d'Alembert wave equation is not valid in two-dimensional space.

A Schrödinger particle of vanishing angular momentum moving freely in two dimensions experiences an attractive force - the quantum anti-centrifugal force - towards its by: