Abstract
In this article, we prove the uniqueness solution of the homogeneous and non-homogeneous heat equation in periodic Sobolev spaces. We do it in a different way from what we did in [3], in this case we perform differential calculus in Hs-per and we take advantage of the immersion and properties of periodic Sobolev spaces. With this proof we gain to visualize the dissipative property of the homogeneous problem and with this we deduce the continuous dependence with respect to the initial data and the uniqueness solution for both cases: homogeneous and non-homogeneous.
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