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Comment: 25 pages
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...
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.
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