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Regularity of the Gurtin-Pipkin equation
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math.FA
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equationsolutionthetagurtin-pipkinprovedregularitycorrespondingdifference
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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 $\theta$.
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