On the boundary value problem for the heat equation in the degenerating domain

2016

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DOI 10.1063/1.4968457
Data confidence 70 medium
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Abstract

In this work, the domain has the peculiarity of degeneration at initial time according to the low x(t) = tω, ω > 1/2. These problems have the great importance for applications. We show that the homogeneous boundary value problem for the heat equation in the degenerating domain has a non-trivial solution in addition to the trivial solution.