Abstract We study the dynamics of a population with an age structure whose range expands time, where adult is assumed to satisfy reaction–diffusion equation over changing interval determined by Stefan type free boundary condition, while juvenile satisfies evolving domain population. The interactions between and populations involve fixed time-delay, which renders model nonlocal in nature. After ...

A free boundary problem for the dynamics of a glasslike binary fluid naturally leads to singular perturbation strongly degenerate parabolic partial differential equation in 1D. We present conjecture an asymptotic formula velocity and prove weak version conjecture. The results are based on analysis family local travelling wave solutions.

Abstract We consider the vectorial analogue of thin free boundary problem introduced by Caffarelli et al. (J Eur math Soc 12:1151-1179, 2010) as a realization nonlocal version classical Bernoulli problem. study optimal regularity, nondegeneracy, and density properties local minimizers. Via blow-up analysis based on Weiss type monotonicity formula, we show that is union “regular” “singular” part...

In this article, we study the behavior of two species evolving in a domain with free boundary. This system mimics spread invasive or new predator species, which boundaries represent expanding fronts and are described by Stefan condition. A priori estimates for required functions established. These used to prove existence uniqueness solution.