Time asymptotics for a critical case in fragmentation and growth-fragmentation equations
نویسندگان
چکیده
منابع مشابه
Time Asymptotics for a Critical Case in Fragmentation and Growth-Fragmentation Equations
Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, when the division rate is constant and the growth rate is linear or zero. The study of these cases may be reduced to the study of the following fragmentation equation: ∂ ∂t u(t,...
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We give here an explicit formula for the following critical case of the growth-fragmentation equation ∂ ∂t u(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...
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ژورنال
عنوان ژورنال: Kinetic and Related Models
سال: 2016
ISSN: 1937-5093
DOI: 10.3934/krm.2016.9.251