Traveling wave solutions for some density dependent diffusion equations. (English) Zbl 0612.35069

Hosono, Yuzo

Japan J. Appl. Math. 3, 163-196 (1986).

Existence and stability of monotone traveling wave solutions of the equation \[ u_ t=(u^ m)_{xx}+f(u),\quad m>1 \] and f(u) vanishes at the three points \(0<\alpha <1\). The asymptotic behaviour of the solutions of the initial value problem is also investigated.

Reviewer: G.Boillat

MSC:

35K55	Nonlinear parabolic equations
35B40	Asymptotic behavior of solutions to PDEs
35B35	Stability in context of PDEs
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
92D25	Population dynamics (general)

Keywords:

population dynamics; Existence; stability; traveling wave; asymptotic behaviour; initial value problem

References:

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