On the characteristic initial value problem for the wave equation in odd spatial dimensions with radial initial data
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The paper obtains an explicit solution of the characteristic initial value problem for the wave equation in odd spatial dimensions with radial initial data via solution of a characteristic boundary value problem involving a singular differential equation. The solution of the latter problem is obtained by a modified Riemann method. It is shown that on the time axis the solution of the original problem reduces to the solution that is obtainable by the use of Asgeirsson’s mean value theorem.
KeywordsDifferential Equation Initial Data Wave Equation Original Problem Spatial Dimension
- R. Courant -D. Hilbert Methods of Mathematical Physics vol. II, Interscience Publishers, New York, 1962.Google Scholar
- A. Weinstein,On the wave equation and Euler-Poisson-Darboux equation, Proc. of the 5th Symposium in Appl. Math., McGraw Hill, New York (1954), pp. 137–147.Google Scholar
- G. Darboux,Theorie Generale des Surfaces, vol. II, Book 4, Gauthier-Villars, Paris, 1889.Google Scholar