ﻻ يوجد ملخص باللغة العربية
We study the dynamics of a one-dimensional non-linear and non-local drift-di usion equation set in the half-line, with the coupling involving the trace value on the boundary. The initial mass M of the density determines the behaviour of the equation: attraction to self similar pro le, to a steady state of nite time blow up for supercritical mass. Using the logarithmic Sobolev and the HWI inequalities we obtain a rate of convergence for the cases subcritical and critical mass. Moreover, we prove a comparison principle on the equation obtained after space integration. This concentration-comparison principle allows proving blow-up of solutions for large initial data without any monotonicity assumption on the initial data.
We address the energy transfer in the differential system $$ begin{cases} u_{ttt}+alpha u_{tt} - beta Delta u_t - gamma Delta u = -eta Delta theta theta_t - kappa Delta theta =eta Delta u_{tt}+ alphaeta Delta u_t end{cases} $$ made by a Moore-Gibson
We introduce and analyze several aspects of a new model for cell differentiation. It assumes that differentiation of progenitor cells is a continuous process. From the mathematical point of view, it is based on partial differential equations of trans
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite critical m
In 1964 J. M. Luttinger introduced a model for the quantum thermal transport. In this paper we study the spectral theory of the Hamiltonian operator associated to the Luttingers model, with a special focus at the one-dimensional case. It is shown tha
This work continues the study of the thermal Hamiltonian, initially proposed by J. M. Luttinger in 1964 as a model for the conduction of thermal currents in solids. The previous work [DL] contains a complete study of the free model in one spatial dim