Traveling front solutions in nonlinear diffusion degenerate Fisher-KPP and Nagumo equations via the Conley index - Adnani, Fatiha El; Alaoui, Hamad Talibi (Topological Methods in Nonlinear Analysis, 2010)
Existence of one dimensional traveling wave solutions u( x,t) :=φ ( x-ct) at the stationary equilibria, for the nonlinear degenerate reaction-diffusion equation u_t=[K( u)u_x]_x+F( u) is studied, where K is the density coefficient and F is the reactive part. We use the Conley index theory to show that there is a traveling front solutions connecting the critical points of the reaction-diffusion equations. We consider the nonlinear degenerate generalized Fisher-KPP and Nagumo equations.