Abstract:
In the article it is shown that the homogeneous Volterra integral equation of the second kind, to
which
the homogeneous boundary value problem of heat conduction in the degenerating domain is reduced,
has a nonzero solution. The boundary of the domain moves with a variable velocity. It is shown that
the norm of the integral operator acting in classes of continuous functions is equal to 1. Mellin
transformation is applied to the obtained integral equation. It is proved that for certain values
of the spectral parameter the
eigenvalues of the integral equation will be simple.
