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Convergence to travelling waves for quasilinear Fisher–KPP type equations

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Díaz Díaz, Jesús Ildefonso and Kamin, S. (2012) Convergence to travelling waves for quasilinear Fisher–KPP type equations. Journal of Mathematical Analysis and Applications, 390 (1). pp. 74-85. ISSN 0022-247X

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022247X12000340


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Abstract

We consider the Cauchy problem ut = ϕ(u)xx + ψ(u), (t, x) ∈ R+ × R, u(0, x) = u0(x), x ∈ R, when the increasing function ϕ satisfies that ϕ(0) = 0 and the equation may degenerate at u = 0 (in the case of ϕ� (0) = 0). We consider the case of u0 ∈ L∞(R), 0 u0(x) 1 a.e. x ∈ R and the special case of ψ(u) = u − ϕ(u). We prove that the solution approaches the travelling wave solution (with speed c = 1), spreading either to the right or to the left, or to the two travelling waves moving in opposite directions.


Item Type:Article
Uncontrolled Keywords:Kolmogorov, Petrovsky and Piscunov equation;Travelling waves; Asymptotic convergence
Subjects:Sciences > Mathematics > Differential equations
ID Code:29589
Deposited On:16 Apr 2015 08:54
Last Modified:12 Dec 2018 15:07

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