We study an initial-boundary value problem of the the heat equation with Heaviside function in the source term equipped with Neumann boundary conditions. This heat equation emerges after linearization of viscous Burgers equation [9, 26]. The first half of the article focuses on the study of associated two initial-boundary value problems and existence of derivative of boundary function introduced along positive t axis due to Heaviside function. The existence of the same is shown with the help of Volterra’s integral equation of first kind. Also, it’s important to highlight that the solutions to two initial-boundary value problems are articulated using Green’s function. The second part of the article studies asymptotic behavior of the solutions to the associated initial-boundary value problems.
