Spreading Speed in A Nonmonotone Equation with Dispersal and Delay

This paper is concerned with the estimation of spreading speed of a nonmonotone equation, which involves time delay and nonlocal dispersal. Due to the time delay, this equation does not generate monotone semiflows when the positive initial value is given. By constructing an auxiliary monotone equation, we obtain the spreading speed when the initial value admits nonempty compact support. Moreover, by passing to a limit function, we confirm the existence of traveling wave solutions if the wave speed equals to the spreading speed, which states the minimal wave speed of traveling wave solutions and improves the known results.

ON THE STABILIZATION OF A VISCOUS BAROTROPIC SELF-GRAVITATING MEDIUM WITH A NONMONOTONE EQUATION OF STATE

We consider the compressible barotropic Navier–Stokes system in one dimension, with a nonmonotone equation of state and self-gravitation. We solve an associated "fixed-free" boundary problem and prove asymptotic properties of the unique globally defined solution for large time. We also comment on a related model of quantum fluid describing the dynamics of nuclear matter with zero temperature and Coulomb effects.