Weak solutions and differentiability for size structured population models

A monotone approximation for the nonautonomous size-structured population model

“…The above problem has been widely investigated [1,2,6,7]. In particular, several numerical methods for approximating the autonomous case of this equation have been developed.…”

Sensitivity equations for a size-structured population model

“…Sample numerical results to illustrate the use of these equations are also presented. [3,4,29,32] have focused on establishing well-posedness and stability analysis of models, formulating schemes for numerical solutions, and parameter estimation of individual rates. However, to the best of our knowledge, thus far there is no literature on sensitivity equations and the related analysis for size-structured population models.…”

“…A semigroup approach is one of the popular and elegant methods used in the literature (e.g., [3,4]) to establish the existence and uniqueness of solutions to size-structured population models. The idea behind this approach is to write the partial differential equation (1) in the abstract forṁ…”

“…However, our efforts in trying to apply this framework to (2) were not productive, as the domain of operator A is dependent on the parameters g and β themselves. For example, the domain of A in [4] is defined as domA = ϕ ∈ H | gϕ ∈ H 1 (0,x), lim x→x (gϕ)(x) = 0, (gϕ)(0) =…”

“…and A : domA ⊂ H → H for an appropriately defined Hilbert space H. The variational approach in [4] provides another method to establish existence and uniqueness of solutions to (1), where a Gelfand triple was constructed as V → H → V * with V = domA * . Here the adjoint operator A * of A is given by…”