Perthame, Benoît; Ryzhik, Lenya Exponential decay for the fragmentation or cell-division equation. (English) Zbl 1072.35195 J. Differ. Equations 210, No. 1, 155-177 (2005). 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. Reviewer: Michael I. Gil’ (Beer-Sheva) Cited in 2 ReviewsCited in 70 Documents MSC: 35R10 Partial functional-differential equations 92C37 Cell biology 35B35 Stability in context of PDEs 35B40 Asymptotic behavior of solutions to PDEs Keywords:stable steady state; asymptotic stability; first positive eigenvector × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Arlotti, L.; Banasiak, J., Strictly substochastic semigroups with application to conservative and shattering solutions to fragmentation equations with mass loss, J. Math. Anal. Appl., 293, 2, 693-720 (2004) · Zbl 1075.47023 [2] Baccelli, F.; McDonald, D. R.; Reynier, J., A mean field model for multiple TCP connections through a buffer implementing RED, (Performance Evaluation, vol. 11 (2002), Elsevier Science: Elsevier Science Amsterdam), 77-97 [3] Basse, B.; Baguley, B. C.; Marshall, E. S.; Joseph, W. R.; van Brunt, B.; Wake, G.; Wall, D. 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