Global attractivity in a non-monotone age-structured model with age-dependent diffusion and death rates

• Published in: Advances in difference equations 2018-11, Vol.2018 (1), p.1-12, Article 419
• Main Author: Al-Jararha, M.
• Format: Article
• Language: English
• Subjects: Age; Age-dependent death rate; Age-dependent diffusion rate; Age-structured model; Analysis; Difference and Functional Equations; Diffusion rate; Functional Analysis; Global attractivity; Homogeneous equilibrium solution; Mathematics; Mathematics and Statistics; Non-monotone birth function; Ordinary Differential Equations; Partial Differential Equations
• ISSN: 1687-1847; 1687-1839; 1687-1847
• DOI: 10.1186/s13662-018-1884-4

In this paper, the global attractivity of the homogeneous equilibrium solution for the diffusive age-structured model { ∂ u ∂ t + ∂ u ∂ a = D ( a ) ∂ 2 u ∂ x 2 − d ( a ) u , t ≥ t 0 ≥ A l > 0 , a ≥ 0 , 0 < x < π , w ( t , x ) = ∫ τ A l u ( t , a , x ) d a , t ≥ t 0 ≥ A l > 0 , 0 < x < π , τ ≥ 0 , u ( t , 0 , x ) = f ( w ( t , x ) ) , t ≥ t 0 ≥ A l > 0 , 0 < x < π , u x ( t , a , 0 ) = u x ( t , a , π ) = 0 , t ≥ t 0 ≥ A l > 0 , a ≥ 0 , is established when the diffusion and death rates, D ( a ) and d ( a ) , respectively, are age dependent during the whole life of the species, and when the birth function f ( w ) is nonmonotone. In the paper, we also present some demonstrative examples.