International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 549-558
doi:10.1155/S0161171280000415
Generalized random processes and Cauchy's problem for some partial differential systems
Faculty of Science, King Abdulaziz University, P.O. Box 1540, Jeddah, Saudi Arabia
Received 1 February 1979; Revised 22 October 1979
Copyright © 1980 Mahmoud M. El-Borai. 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 this paper we consider a parabolic partial differential system of the form DtHt=L(t,x,D)Ht. The generalized stochastic solutions Ht, corresponding to the generalized stochastic initial conditions H0 are given. Some properties concerning these generalized stochastic solutions are also obtained.