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Comment: 57 pages, published version
Comment: 32 pages, 1 figure
Comment: To appear in SIAM Journal of Applied Mathematics
The Hubble constant proves to be the pseudo-Finsleroid--Landsberg factor. The
covariantly conserved pseudo-Finsleroid--gravitational tensor is explicitly
found after evaluating the respective Finsleroid--case curvature tensor and
required contractions in attentive way. The equations arisen involve one
parameter g of extension which measures the Finslerian deviation of the
curvature of the indicatrix of unit vectors. The vector field b^i(x) of the
axes of the pseudo--Finsleroids is naturally identified to the field of average
velocity vectors of matter of the universe. The consistent (and unique)
continuation of the Robertson--Walker metric, and hence the Friedmann metrics,
in the Finslerian domain with respect to the parameter g is arisen. The
cosmological pressure and energy density prove to be linear functions of g^2,
so that the p...
Comment: 38 pages, LaTeX2e, 0 figures
This paper presents an observation that under reasonable conditions, many
partial differential equations from mathematical physics possess three
structural properties. One of them can be understand as a variant of the
celebrated Onsager reciprocal relation in Modern Thermodynamics. It displays a
direct relation of irreversible processes to the entropy change. We show that
the properties imply various entropy dissipation conditions for hyperbolic
relaxation problems. As an application of the observation, we propose an
approximation method to solve relaxation problems. Moreover, the observation is
interpreted physically and verified with eight (sets of) systems from different
fields.
