On spectral gaps of growth-fragmentation semigroups with mass loss or death
On spectral gaps of growth-fragmentation semigroups with mass loss or death
<p style='text-indent:20px;'>We give a general theory on well-posedness and time asymptotics for growth fragmentation equations in <inline-formula><tex-math id="M1">\begin{document}$ L^{1} $\end{document}</tex-math></inline-formula> spaces. We prove first generation of <inline-formula><tex-math id="M2">\begin{document}$ C_{0} $\end{document}</tex-math></inline-formula>-semigroups governing them for unbounded total fragmentation rate and fragmentation kernel <inline-formula><tex-math id="M3">\begin{document}$ b(.,.) $\end{document}</tex-math></inline-formula> such that <inline-formula><tex-math id="M4">\begin{document}$ \int_{0}^{y}xb(x,y)dx = …