Asymptotic stability of traveling waves with critical speed for a double degenerate Fisher type equation

This paper is concerned with the asymptotic stability of traveling waves with the critical speed for a double degenerate Fisher type equation. By applying point-wise Green's function approach with detailed and special integral and semigroup estimates, we prove the linear and nonlinear asymptotic stability of the wave with the critical speed in some polynomially weighted spaces; and show that the decay of the semigroup can be in order of t − 2 or faster than t − 1 , and the decay of the perturbation of the wave in time can be in order of t − θ for some θ ∈ ( 0 , 1 ] . In this paper, we also prove the spectral stability of the wave with the critical speed in some exponentially and polynomially weighted spaces.