Strong and weak properties of travelling waves for degenerate diffusion/aggregation-diffusion models with non-smooth reaction term

Abstract In this paper, we investigate a degenerate reaction–diffusion/reaction–aggregation–diffusion model with non-smooth reaction term. The strong and weak properties of travelling wave front solutions for this model are analyzed. Under degenerate reaction–diffusion/reaction–aggregation–diffusion term and non-smooth reaction term, we obtain how strong and weak properties change.

[1]  J. G. Skellam.  Random dispersal in theoretical populations , 1951, Biometrika.

[2]  Arturo de Pablo,et al.  Travelling wave behaviour for a Porous-Fisher equation , 1998, European Journal of Applied Mathematics.

[3]  Cristina Marcelli,et al.  Fastness and continuous dependence in front propagation in Fisher-KPP equations , 2008 .

[4]  Pavel Drábek,et al.  Convergence to travelling waves in Fisher’s population genetics model with a non-Lipschitzian reaction term , 2017, Journal of mathematical biology.

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

[6]  R M Nisbet,et al.  The regulation of inhomogeneous populations. , 1975, Journal of theoretical biology.

[7]  H. G. Landau,et al.  Nonlinear Parabolic Equations , 1948 .

[8]  N. Shigesada,et al.  Spatial segregation of interacting species. , 1979, Journal of theoretical biology.

[9]  D. Morale,et al.  An interacting particle system modelling aggregation behavior: from individuals to populations , 2005, Journal of mathematical biology.

[10]  Faustino Sánchez-Garduño,et al.  Existence and uniqueness of a sharp travelling wave in degenerate non-linear diffusion Fisher-KPP equations , 1994 .

[11]  Faustino Sánchez-Garduño,et al.  A non-linear degenerate equation for direct aggregation and traveling wave dynamics , 2009 .

[12]  Vı́ctor Padrón,et al.  Effect of aggregation on population recovery modeled by a forward-backward pseudoparabolic equation , 2003 .

[13]  Yong-Jung Kim,et al.  Inviscid traveling waves of monostable nonlinearity , 2017, Appl. Math. Lett..

[14]  Luisa Malaguti,et al.  Sharp profiles in degenerate and doubly degenerate Fisher-KPP equations , 2003 .

[15]  Peter Grindrod,et al.  Models of individual aggregation or clustering in single and multi-species communities , 1988 .

[16]  Zhengfang Zhou,et al.  Traveling wave in backward and forward parabolic equations from population dynamics , 2014 .

[17]  Serena Matucci,et al.  AGGREGATIVE MOVEMENT AND FRONT PROPAGATION FOR BI-STABLE POPULATION MODELS , 2007 .

[18]  A. Tsoularis,et al.  Analysis of logistic growth models. , 2002, Mathematical biosciences.

[19]  Jonathan A. Sherratt,et al.  On the Form of Smooth-Front Travelling Waves in a Reaction-Diffusion Equation with Degenerate Nonlinear Diffusion , 2010 .

[20]  Peter Grindrod,et al.  Weak travelling fronts for population models with density dependent dispersion , 1987 .