Geodesic
Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation
Marie Doumic1 ; Bruce van Brunt2
1Sorbonne Universités, Inria, UPMC Univ Paris 06, Lab. J.L. Lions UMR CNRS 7598, Wolfgang Pauli Institute, University of Vienna, Paris, Vienna, France, Austria
2Institute 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

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