Regularity of the Gurtin-Pipkin equation

Abstract

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 $\theta$.

9 pages, 10 references. In the new version typos are corrected and results about strong solutions is added

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