A nonlinear boundary value problem arising in growing cell populations

A stationary modified version of Rotenberg's model is analyzed. The transition rate and the total transition cross section is allowed to depend on the density of population. The existence and uniqueness theorems for the equation v∂ψ/∂μ(μ,v)+λψ(μ, v)+σ(μ,v,ψ(μ,v)) = ∫abr(μ,v,v′,ψ(μ,v′))dv′ is presented, supplemented with the boundary condition ψ|Γ(0) = K(ψ|Γ(1)). The functional setting is Lp-spaces (1≤p<∞) to fit with the more appropriate framework L1([0,1]×[a,b];dμdv) where ψ(μ,v) has the meaning of a density of the population with respect to the degree of maturation μ and the maturation velocity v.