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arXiv · 2006.08984

On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions

Alexander Polkovnikov
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Abstract

We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in ${\mathbb R}^n $ with non-coercive boundary conditions. In this case there is a loss of smoothness of the solution in Sobolev type spaces compared with the coercive situation. Using by Faedo-Galerkin method we prove that problem has unique solution in special Bochner space.

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Alexander Polkovnikov. 2020-06-16. On initial boundary value problem for parabolic differential operator with non-coercive boundary conditions. https://arxiv.org/abs/2006.08984

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