Glasgow Mathematical Journal

Table of Contents - 1969 - Volume 10, Issue 02  

Research Article

Riemann's method and the characteristic value and cauchy problems for the damped wave equation†

Eutiquio C. Younga1

a1 Florida State University Tallahassee, Florida 32306

Riemann's method for solving the Cauchy problem for hyperbolic differential equations in two independent variables has been extended in a number of papers [4], [5], [2] to the wave equation in space of higher dimensions. The method, which consists in the determination of a so-called Riemann function, hinges on the solution of a characteristic value problem. Accordingly, if Riemann's method is to be used in solving a characteristic value problem, one will have to consider another characteristic value problem and thus the process becomes circular. This difficulty was first overcome by Protter [7] in solving the characteristic value problem for the wave equation in three variables. There he employed a variation of Riemann's method developed by Martin [5]. Martin's result was later extended by Diaz and Martin [2] to the wave equation in an arbitrary number of variables. This made it possible to extend Protter's result to the wave equation in space of higher dimensions [8].

(Received July 06 1968)

Footnotes

† This research was supported by NSF research grant GP 7457.