On the initial value problem for a partial differential equation with operator coefficients

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.