New Results on a Partial Differential Equation with General Piecewise Constant Argument

Abstract

There have been very few analyses on partial differential equations with piecewise constant arguments and as far as we know, there is no study conducted on heat equation with piecewise constant argument of generalized type. Motivated by this fact, this study aims to solve and analyse heat equation with piecewise constant argument of generalized type. We obtain formal solution of heat equation with piecewise constant argument of generalized type by separation of variables. We apply the Laplace transform method using unit step function and method of steps on each consecutive intervals. We investigate stability, oscillation, boundedness properties of solutions.