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.