International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 3, Pages 549-558

Generalized random processes and Cauchy's problem for some partial differential systems

Mahmoud M. El-Borai

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.


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.