On a non-linear size-structured population model. (English) Zbl 1440.35332
Summary: This paper deals with a size-structured population model consisting of a quasi-linear first-order partial differential equation with nonlinear boundary condition. The existence and uniqueness of solutions are firstly obtained by transforming the system into an equivalent integral equation such that the corresponding integral operator forms a contraction. Furthermore, the existence of global attractor is established by proving the asymptotic smoothness and eventual compactness of the nonlinear semigroup associated with the solutions. Finally, we discuss the uniform persistence and existence of compact attractor contained inside the uniformly persistent set.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35L03 | Initial value problems for first-order hyperbolic equations |
| 35B41 | Attractors |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 92D25 | Population dynamics (general) |
Keywords:
size-structure; existence; uniqueness; global attractor; uniform persistence; asymptotic smoothnessReferences:
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