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Published **1982**
by Cambridge University Press in Cambridge [Cambridgeshire], New York .

Written in English

- Differential equations, Hyperbolic,
- Boundary value problems,
- Wave equation

**Edition Notes**

Statement | Reiko Sakamoto ; translated by Katsumi Miyahara. |

Classifications | |
---|---|

LC Classifications | QA377 .S2713 1982 |

The Physical Object | |

Pagination | viii, 210 p. ; |

Number of Pages | 210 |

ID Numbers | |

Open Library | OL4258339M |

ISBN 10 | 0521235685 |

LC Control Number | 81003865 |

Abstract Boundary value problems for steady-state ﬂow in elastoplasticity are a topic of mathematical and physical interest. In particular, the underlying PDE may be hyperbolic, and uncertainties surround the choice of physically appropriate stress and velocity boundary conditions. The well-posedness of hyperbolic initial boundary value problems is linked to the occurrence of zeros of the so-called Lopatinski˘ı determinant. For an important class of problems, the Lopatinski˘ı determinant vanishes in the hyperbolic region of the frequency domain and nowhere else. In this paper, we give a criterion that ensures. estimates for mixed initial-boundary value problems for certain hyperbolic partial differential equations in regions with corners. The work will revolve around the introduction of a new symmetrizer for general initial-boundary value problems. This symmetrizer seems to have a significance of its own. Boundary value problems. Differential equations, Hyperbolic. Gas dynamics. Bibliographic information. Publication date Note Page following t.p. has title in Chinese. Figures in pocket. Browse related items. Start at call number: QAL5 View full page.

on adjacent faces are usually di erent, so the initial boundary value problem is of mixed type because of the change in boundary condition. In spatial dimension d= 3 the external corner is a meeting point of three or-thogonal faces making a trihedral angle. The study of hyperbolic problems in such regions is very little developed. discontinuous solutions for hyperbolic problems. An example of a discontinuous solution is a shock wave, which is a feature of solutions of nonlinear hyperbolic equations. To illustrate further the concept of characteristics, consider the more general hyper-bolic equation ut +aux +bu=f(t,x), u(0,x)=u0(x), () where a and b are constants. This paper is devoted to initial boundary value problems for quasi-linear symmetric hyperbolic systems in a domain with characteristic boundary. It extends the theory on linear symmetric hyperbolic systems established by Friedrichs to the nonlinear case. With boundary value problems we will have a differential equation and we will specify the function and/or derivatives at different points, which we’ll call boundary values. For second order differential equations, which will be looking at pretty much exclusively here, any of the following can, and will, be used for boundary conditions.

The Second Edition presents hyperbolic equations in great detail as well as new coverage on second-order systems of wave equations including acoustic waves, elastic waves, and Einstein equations. Compared to first-order hyperbolic systems, initial-boundary value problems for such systems contain new properties that must be taken into account when analyzing stability. Hyperbolic nonconservative partial differential equations, such as the Von Foerster system, in which boundary conditions may depend upon the dependent variable (integral boundary conditions, for example) are solved by an approximation method based on similar work of the author for (nonlinear stochastic) ordinary differential equations. () Spectral methods for hyperbolic initial boundary value problems on parallel computers. Journal of Computational and Applied Mathematics , () Towards a transparent boundary condition for compressible Navier-Stokes equations. The book discusses problems on the derivation of equations and boundary condition. These Problems are arranged on the type and reduction to canonical form of equations in two or more independent variables. The equations of hyperbolic type concerns derive from problems on vibrations of continuous media and on electromagnetic oscillations.

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