On the characteristic initial value problem for the wave equation in odd spatial dimensions with radial initial data

1972 ◽  
Vol 94 (1) ◽  
pp. 161-176 ◽  
Author(s):  
J. B. Diaz ◽  
E. C. Young
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Initial Value Problem ◽  
Initial Value ◽  
Spatial Dimensions ◽  
Characteristic Initial Value Problem

Numerical relativity. I. The characteristic initial value problem

1982 ◽  
Vol 384 (1787) ◽  
pp. 427-454 ◽  
Keyword(s):  
Initial Data ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Numerical Relativity ◽  
Hyperbolic Systems ◽  
Systems Of Equations ◽  
Initial Value ◽  
Hyperbolic Systems Of Equations ◽  
Characteristic Initial Value Problem

In this, the first of a series of papers on numerical relativity, the characteristic initial value problem is posed in a form suitable for numerical integration. It can be reduced to the solution of two initial value problems for sets of ordinary differential equations (on the initial surfaces) and the solution of two initial value problems for hyperbolic systems of equations, one linear, one quasilinear. The initial data may be specified freely. Subsequent papers will develop numerical solutions of Einstein’s equations with use of this formalism.

Reduction of the characteristic initial value problem to the Cauchy problem and its applications to the Einstein equations

1990 ◽  
Vol 427 (1872) ◽  
pp. 221-239 ◽  
Keyword(s):  
Cauchy Problem ◽  
Perfect Fluid ◽  
Initial Value Problem ◽  
Einstein Equations ◽  
Initial Value ◽  
Fluid Source ◽  
Null Hypersurfaces ◽  
The Cauchy Problem ◽  
Well Posed ◽  
Characteristic Initial Value Problem

A method is described by means of which the characteristic initial value problem can be reduced to the Cauchy problem and examples are given of how it can be used in practice. As an application it is shown that the characteristic initial value problem for the Einstein equations in vacuum or with perfect fluid source is well posed when data are given on two transversely intersecting null hypersurfaces. A new discussion is given of the freely specifiable data for this problem.

scholarly journals Nonanalytic solutions of the KdV equation

2004 ◽  
Vol 2004 (6) ◽  
pp. 453-460 ◽  
Author(s):  
Peter Byers ◽  
A. Alexandrou Himonas
Keyword(s):  
Initial Data ◽  
Initial Value Problem ◽  
Kdv Equation ◽  
Initial Value ◽  
The Kdv Equation

We construct nonanalytic solutions to the initial value problem for the KdV equation with analytic initial data in both the periodic and the nonperiodic cases.

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