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

摘要

In this work, the domain has the peculiarity of degeneration at initial time according to the low x(t)= t~w, w > 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.