By Garcia J., De Lis C. S.

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**Extra info for A bifurcation problem governed by the boundary condition I***

**Sample text**

The Hubble constant It is amusing that the entire ‘dramatic clash of ideas’ of the last 20 years in connection with the determination of the value of the Hubble constant takes root at the very beginning of the 1980s (but was discernible even before that), when Sandage and Tammann, and practically at the same time de Vaucouleurs, arrived at two mutually exclusive estimates of the value of H0 . According to Sandage and Tammann (1982), H0 = 50 km s−1 Mpc−1 . According to de Vaucouleurs (1982), the constant was twice as large, H0 = 90–100 km s−1 Mpc−1 .

4) × f e (t, x, q ) f (t, x, p )[1 + f (t, x, p)] − f e (t, x, q) f (t, x, p)[1 + f (t, x, p )] , where |M|2 is the matrix element for the Compton scattering of quanta by electrons, δ (4) ( p) is the Dirac delta function, f (t, x, p) is the photon distribution function, and f e (t, x, q) is the electron distribution function. Again following the work of Hu and colleagues (Hu, 1995; Hu and Silk, 1993; Hu, Scott and Silk, 1994) we consider the equilibrium distribution of electrons over momentum q in the neighbourhood of a certain mean value of m e ve that describes possible large-scale matter fluxes.

The left-hand side of Eq. 1) describes the free distribution of photons in the absence of collisions and external sources: df ∂f ∂ f dx μ ∂ f dγ μ ∂ f d p0 = + μ + + . 3) The following notation was used in this equation: γ μ = a( p μ / p), p 2 = pi pi and dx μ /dt = ˙ p μ / p 0 ; d p 0 /dt = −(a/a) p. For a uniform and, on average, isotropic Universe, only the first and the last terms on the right-hand side of Eq. 3) are non-zero. Let us turn to analysing the collision integral for Compton processes.

### A bifurcation problem governed by the boundary condition I* by Garcia J., De Lis C. S.

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