Geodesic
Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation
Marie Doumic1 ; Bruce van Brunt2
1 Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598, Wolfgang Pauli Institute, University of Vienna, Paris, Vienna, France, Austria
2 Institute of Fundamental Sciences, Massey University, New Zealand
ESAIM. Proceedings, Tome 62 (2018), pp. 30-42.

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We give here an explicit formula for the following critical case of the growth-fragmentation equation ∂/∂tu(t,x)+∂/∂x(gxu(t,x))+bu(t,x)=bα2u(t,αx),        u(0,x)=u0(x) ∂∂tu(t,x)+∂∂x(gxu(t,x))+bu(t,x)=bα2u(t,αx),        u(0,x)=u0(x) for some constants g > 0, b > 0 and α >1 - the case α = 2 being the emblematic binary fission case. We discuss the links between this formula and the asymptotic ones previously obtained in [8], and use them to clarify how periodicity may appear asymptotically.
DOI : 10.1051/proc/201862030

Marie Doumic 1 ; Bruce van Brunt 2

1 Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598, Wolfgang Pauli Institute, University of Vienna, Paris, Vienna, France, Austria
2 Institute of Fundamental Sciences, Massey University, New Zealand 
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     title = {Explicit {Solution} and {Fine} {Asymptotics} for a {Critical} {Growth-Fragmentation} {Equation}},
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Marie Doumic; Bruce van Brunt. Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation. ESAIM. Proceedings, Tome 62 (2018), pp. 30-42. doi : 10.1051/proc/201862030. http://geodesic.mathdoc.fr/articles/10.1051/proc/201862030/

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