Propagation dynamics of nonlocal dispersal equations with inhomogeneous bistable nonlinearity

<p style='text-indent:20px;'>This paper is concerned with the nonlocal dispersal equations inhomogeneous bistable nonlinearity in one dimension. The varying consists of two spatially independent nonlinearities, which are connected by a compact transition region. We establish existence unique entire solution connecting traveling wave solutions pertaining to different nonlinearities. In particular, we use "squeezing" technique show that equation approaching from infinity, after going through region, converges other prescribed on side. Furthermore, also prove such an Lyapunov stable.</p>