**H. Leszczynski**

## Quasi-Linearisation Methods for a Non-Linear Heat Equation with Functional Dependence

**abstract:**

A heat equation is consodered with the non-linear right-hand side which
depends on certain Volterra-type functionals acting on the unknown
function and on its gradient.
Some natural sufficient conditions are given for the existence
and uniqueness of solutions to this equation. The solution is obtained
as a limit of a fast convergent sequence of successive approximations
obtained by the quasi-linearisation method.