International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 1, Pages 103-111
doi:10.1155/S0161171280000075
On the initial value problem for a partial differential equation with operator coefficients
Department of Mathematics, King Abdulaziz University, P.O. Box 1540, Jeddah, Saudi Arabia
Received 15 May 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 the present work it is studied the initial value problem for an equation of the form L∂ku∂tk=∑j=1kLj∂k−ju∂tk−j,where L is an elliptic partial differential operator and (Lj:j=1,…,k) is a family of partial differential operators with bounded operator coefficients in a suitable function space. It is found a suitable formula for solution. The correct formulation of the Cauchy problem for this equation is also studied.