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

On the theory of inhomogeneous Bose-Einstein condensation of magnons in yttrium garnet