具有非强制边界条件的抛物型微分算子的初边值问题

IF 0.4 Q4 MATHEMATICS

Journal of Siberian Federal University-Mathematics & Physics Pub Date : 2020-06-16 DOI:10.17516/1997-1397-2020-13-5-547-558

A. Polkovnikov

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引用次数: 0

摘要

在非强制边界条件下，研究了Rn柱面上二阶一致2-抛物型微分算子的初边值问题。在这种情况下，与强制情况相比，Sobolev型空间中解的光滑性有所损失。利用Faedo-Galerkin方法证明了该问题在特殊Bochner空间中具有唯一解

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On Initial Boundary Value Problem for Parabolic Differential Operator with Non-coercive Boundary Conditions

We consider initial boundary value problem for uniformly 2-parabolic differential operator of second order in cylinder domain in Rn 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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来源期刊

Journal of Siberian Federal University-Mathematics & Physics MATHEMATICS-

CiteScore

0.90

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0.00%

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