On the proximity of solutions of unperturbed and hyperbolized heat equations for discontinuous initial data

In this paper we investigate the effect of the additive in the form of a second time derivative with a small parameter $\varepsilon$ in the heat equation for discontinuous periodic initial data. It is shown that, with the exception of the initial instants of time, the error of hyperbolization tends to zero as the square root of the value of the additive.