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

Published online by Cambridge University Press:  18 May 2009

Eutiquio C. Young
Eutiquio C. Young
Affiliation:
Florida State UniversityTallahassee, Florida32306
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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].

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 10 , Issue 2 , July 1969, pp. 147 - 152
Copyright
Copyright © Glasgow Mathematical Journal Trust 1969

References

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