Narrow Results

We consider the cell division equation which describes the continuous growth of cells and their division in two pieces. Growth conserves the total number of cells while division conserves the total mass of the system but increases the number of cells. We give general assumptions on the coefficient so that we can prove the existence of a solution (λ, N, ϕ) to the related eigenproblem. We also prove that the solution can be obtained as the sum of an explicit series. Our motivation, besides its applications to the biology and fragmentation, is that the eigenelements allow to prove a priori estimates and long-time asymptotics through the General Relative Entropy.¹⁶.