Exponential decay for the fragmentation or cell-division equation
The authors consider the equation \[ \partial n(t, x)/\partial t+\partial n(t, x)/\partial x+ b(x)n(t, x)=4b(2x)n(t, 2x), t>0, x\geq 0 \] with the corresponding initial and boundary conditions. Here \(b\) is a given function. This equation is classical. It arises in various applications as a model for cell-division or fragmentation. In biology, it describes the evolution of the density of cells that grow and divide. The authors prove the existence of a stable steady distribution (first positive eigenvector) under general assumptions in the variable coefficients case. It is also investigated the exponential convergence, for large times, of solutions toward such a steady state.
scientific article; zbMATH DE number 2136783