Regularity of the Gurtin-Pipkin equation
  We study regularity of the solution $\theta$ to the Gurtin-Pipkin integral-differential equation of the first order in time. The solution smoothness in Sobolev spaces is proved. Also it is proved that the 'perturbation' part, namely, the difference of $\theta$ and the solution to the corresponding wave equation is smoother than $\theta$. 
Sergei A. Ivanov
math.FA