Global stability for the prion equation with general incidence

Abstract

We consider the so-called prion equation with the general incidence term introduced in [Greer et al., 2007], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [Gabriel, 2012]. The argument combines a recent spectral gap result for the growth-fragmentation equation in weighted $L^1$ spaces and the analysis of a nonlinear system of three ordinary differential equations.

References in corpus (7)

• Rate of convergence to an asymptotic profile for the self-similar fragmentation and growth-fragmentation equations
• Fine asymptotics of profiles and relaxation to equilibrium for growth-fragmentation equations with variable drift rates
• Rate of convergence to self-similarity for the fragmentation equation in L^1 spaces
• Long-time Asymptotics for Nonlinear Growth-fragmentation Equations
• The Shape of the Polymerization Rate in the Prion Equation
• Exponential relaxation to self-similarity for the superquadratic fragmentation equation
• Spectral analysis of semigroups and growth-fragmentation equations

Cited by in corpus (4)

• Spectral gap for the growth-fragmentation equation via Harris's Theorem
• Asymptotic behavior of the growth-fragmentation equation with bounded fragmentation rate
• Existence of Global Classical and Weak Solutions to a Prion Equation with Polymer Joining
• Uniqueness of Weak Solutions to a Prion Equation with Polymer Joining