We are concerned with a class of degenerate diffusion equations time delay describing population dynamics age structure. In our recent study [Nonlinearity, 33 (2020), 4013–4029], we established the existence and uniqueness critical traveling wave for time-delayed equations, obtained reducing mechanism on speed. this paper, now able to show asymptotic spreading speed its coincidence $$c^*(m,r)$$...

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory