Critical sharp front for doubly nonlinear degenerate diffusion equations with time delay

This paper is concerned with the critical sharp traveling wave for doubly nonlinear diffusion equation with time delay, where the doubly nonlinear degenerate diffusion is defined by (∣

[1]  Joseph W.-H. So,et al.  DIRICHLET PROBLEM FOR THE DIFFUSIVE NICHOLSON'S BLOWFLIES EQUATION , 1998 .

[2]  Sergei I. Trofimchuk,et al.  Global continuation of monotone wavefronts , 2012, J. Lond. Math. Soc..

[3]  Xingfu Zou,et al.  A reaction–diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[4]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[5]  Chunhua Ou,et al.  Global Stability of Monostable Traveling Waves For Nonlocal Time-Delayed Reaction-Diffusion Equations , 2010, SIAM J. Math. Anal..

[6]  J. V'azquez,et al.  The Fisher-KPP problem with doubly nonlinear diffusion , 2016, 1601.05718.

[7]  Klaus W. Schaaf.  Asymptotic behavior and traveling wave solutions for parabolic functional-differential equations , 1987 .

[8]  Jingxue Yin,et al.  Variational approach of critical sharp front speeds in degenerate diffusion model with time delay , 2019, Nonlinearity.

[9]  Teresa Faria,et al.  Nonmonotone travelling waves in a single species reaction–diffusion equation with delay , 2005, math/0508098.

[10]  R. Fisher.  THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES , 1937 .

[11]  Jingxue Yin,et al.  Sharp oscillatory traveling waves of structured population dynamics model with degenerate diffusion , 2020, Journal of Differential Equations.

[12]  James D. Murray.  Mathematical Biology: I. An Introduction , 2007 .

[13]  Chi-Tien Lin,et al.  Exponential Stability of Nonmonotone Traveling Waves for Nicholson's Blowflies Equation , 2014, SIAM J. Math. Anal..

[14]  Mimmo Iannelli,et al.  A class of nonlinear diffusion problems in age-dependent population dynamics☆ , 1983 .

[15]  R. Benguria,et al.  Variational Characterization of the Speed of Reaction Diffusion Fronts for Gradient Dependent Diffusion , 2017, Annales Henri Poincaré.

[16]  Michael Y. Li,et al.  Asymptotic stability of travelling waves for Nicholson's blowflies equation with diffusion , 2004, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[17]  I-Liang Chern,et al.  Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay , 2015 .

[18]  Morton E. Gurtin,et al.  On the diffusion of biological populations , 1977 .

[19]  S. P. Blythe,et al.  Nicholson's blowflies revisited , 1980, Nature.

[20]  Benguria,et al.  Variational principle for the asymptotic speed of fronts of the density-dependent diffusion-reaction equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Chunhua Jin,et al.  Existence and Stability of Traveling Waves for Degenerate Reaction–Diffusion Equation with Time Delay , 2018, J. Nonlinear Sci..

[22]  Jingxue Yin,et al.  Traveling waves for time-delayed reaction diffusion equations with degenerate diffusion , 2018, Journal of Differential Equations.

[23]  R. Benguria,et al.  Variational characterization of the speed of propagation of fronts for the nonlinear diffusion equation , 1994, patt-sol/9408001.

[24]  D. Aronson,et al.  Density-Dependent Interaction–Diffusion Systems , 1980 .

[25]  D. Sulsky,et al.  Time delays in age-structured populations. , 1989, Journal of theoretical biology.