Abstract

In the present work it is studied the initial value problem for an equation of the form Lkutk=j=1kLjkjutkj,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.