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arXiv · 1105.1487

On prescribed change of profile for solutions of parabolic equations

Nikolai Dokuchaev
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Abstract

Parabolic equations with homogeneous Dirichlet conditions on the boundary are studied in a setting where the solutions are required to have a prescribed change of the profile in fixed time, instead of a Cauchy condition. It is shown that this problem is well-posed in L_2-setting. Existence and regularity results are established, as well as an analog of the maximum principle.

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Nikolai Dokuchaev. 2011-05-08. On prescribed change of profile for solutions of parabolic equations. https://doi.org/10.1088/1751-8113/44/22/225204

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