  The Bose-Einstein condensation (BEC) of magnons created by a strong pumping
in ferromagnetic thin films of yttrium iron garnet used as systems of finite
size is considered analytically. Such a peculiarity, typical for this magnetic
material, as the presence of a minimum in the spectrum of spin waves at a
finite value of the wave vector is taken into account. The definition of
hightemperature BEC is introduced and its characteristics are discussed. A role
of boundary conditions for spin variables is analyzed, and it is shown that in
the case of free spins on the boundary the magnon lattice can form in the
system. The factors responsible for its appearance are discussed.
