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 Cet article a éte moissonné depuis la source EDP Sciences

Voir la notice de l'article

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 
@article{EP_2018_62_a3,
     author = {Marie Doumic and Bruce van Brunt},
     title = {Explicit {Solution} and {Fine} {Asymptotics} for a {Critical} {Growth-Fragmentation} {Equation}},
     journal = {ESAIM. Proceedings},
     pages = {30--42},
     year = {2018},
     volume = {62},
     doi = {10.1051/proc/201862030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201862030/}
}
TY  - JOUR
AU  - Marie Doumic
AU  - Bruce van Brunt
TI  - Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation
JO  - ESAIM. Proceedings
PY  - 2018
SP  - 30
EP  - 42
VL  - 62
UR  - http://geodesic.mathdoc.fr/articles/10.1051/proc/201862030/
DO  - 10.1051/proc/201862030
LA  - en
ID  - EP_2018_62_a3
ER  - 
%0 Journal Article
%A Marie Doumic
%A Bruce van Brunt
%T Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation
%J ESAIM. Proceedings
%D 2018
%P 30-42
%V 62
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201862030/
%R 10.1051/proc/201862030
%G en
%F EP_2018_62_a3
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

Cité par Sources :