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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.
We study the motion of an incompressible, inviscid two-dimensional fluid in a rotating frame of reference. There the fluid experiences a Coriolis force, which we assume to be linearly dependent on one of the coordinates. This is a common approximatio
In this paper we consider the problem: $partial_{t} u- Delta u=f(u),; u(0)=u_0in exp L^p(R^N),$ where $p>1$ and $f : RtoR$ having an exponential growth at infinity with $f(0)=0.$ We prove local well-posedness in $exp L^p_0(R^N)$ for $f(u)sim mbox{e}^
We study the Lipschitz stability in time for $alpha$-dissipative solutions to the Hunter-Saxton equation, where $alpha in [0,1]$ is a constant. We define metrics in both Lagrangian and Eulerian coordinates, and establish Lipschitz stability for those metrics.
We prove global well-posedness for 3D Dirac equation with a concentrated nonlinearity.
The Degasperis-Procesi equation can be derived as a member of a one-parameter family of asymptotic shallow water approximations to the Euler equations with the same asymptotic accuracy as that of the Camassa-Holm equation. In this paper, we study the