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

Mahmoud M. El-Borai

 Department of Mathematics, King Abdulaziz University, P.O. Box 1540, Jeddah, Saudi Arabia
Received 15 May 1979

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.