Abstract and Applied Analysis

Volume 2004 (2004), Issue 4, Pages 315-335

doi:10.1155/S1085337504306111

## New singular solutions of Protter's problem for the 3 D wave equation

# M. K. Grammatikopoulos,^{1} N. I. Popivanov,^{2} and T. P. Popov^{2}

^{1}Department of Mathematics, University of Ioannina, Ioannina 45110, Greece^{2}Department of Mathematics and Informatics, University of Sofia, Sofia 1164, Bulgaria

Received 10 September 2002

Copyright © 2004 M. K. Grammatikopoulos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In 1952, for the wave equation,Protter formulated some boundary
value problems (BVPs), which are multidimensional
analogues of Darboux problems on the plane. He studied these
problems in a