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Traveling Waves and Global Stability to Time-Delayed Reaction-Diffusion Equations with Degenerate Diffusion

Abstract: In this talk, I will present our current research results on traveling waves for time-delayed reaction-diffusion equations with degeneracy. Different from the existing studies where there exists a minimum wave speed for the traveling waves in the case of mono-stable type equations like Fisher-KPP, we recognize that, for the local reaction-diffusion equations with degenerate diffusion and time-delay, there is no traveling wave with minimum speed, namely, the waves exist only for all speed c>0, but not for c<0 nor c=0. The global stability in L^1-weighted space is also proved. This talk is based on our two recent papers joint with Rui Huang, Chunhua Ji, Jingxue Yin published in J. Nonlinear Sci. (2018), and joint with Tianyuan Xu, Shanming Ji and Jingxue Yin in J. Diff. Eqn. (2018).