Delay partial differential equations

A delay partial differential equation (DPDE) is an equation which involves: (1) at least two independent variables, (2) an unknown function of the independent variables, (3) the behavior of the unknown function at some prior value(s) of the independent variable(s), (4) partial derivative(s) of the unknown function with respect to the independent variable(s).Therefore, a delay partial differential equation differs from a partial differential equation in that it depends not only on the solution at a present stage but also on the solution at some past stage(s). If, additionally, the equation depends on the derivative(s) of the solution at some past stage(s), then it is a neutral delay partial differential equation.Delay partial differential equations are also called partial functional differential equations as their unknown solutions are used in these equations as functional arguments.