Research Article
Long Time Behavior of Solution to Equal Mitosis PDE
Meas Len*
Issue:
Volume 11, Issue 5, October 2025
Pages:
71-77
Received:
17 September 2025
Accepted:
9 October 2025
Published:
19 December 2025
DOI:
10.11648/j.ijtam.20251105.11
Downloads:
Views:
Abstract: In this work, we are interested in the long time behavior of a solution to equal mitosis partial differential equation with positive and periodic coefficients. First, we prove the existence and uniqueness of solution of Floquet eigenvalue and its adjoint eigenvalue problem to the equal mitosis equation by using the fixed point theorem in the suitable L1 weighted space under general division rate hypotheses. Let us recall that the Floquet exponent measures the growth rates of the population and understanding an eigenfunction is crucial for proving the long run behavior of the Cauchy problem. Then we apply the generalized relative entropy method to derive such long time asymptotic behavior of the population density.
Abstract: In this work, we are interested in the long time behavior of a solution to equal mitosis partial differential equation with positive and periodic coefficients. First, we prove the existence and uniqueness of solution of Floquet eigenvalue and its adjoint eigenvalue problem to the equal mitosis equation by using the fixed point theorem in the suitab...
Show More
