Within a recently developed axiomatic formalism for construction of st
ochastic field equations of motion a new form of the equation for damp
ed dynamics of magnetization in ferromagnets is proposed. It takes int
o account spatially inhomogeneous dissipation due to exchange interact
ions and replaces the customary dissipation constant (due to relativis
tic effects) by a dissipation operator. This operator is constructed h
ere by comparison of the resultant phenomenological spin wave spectra
with results of microscopic calculations. Dynamic description of relax
ation of the modulus of magnetization is discussed.