Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617529 | Journal of Mathematical Analysis and Applications | 2012 | 12 Pages |
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)=0φ(0)=0 and the equation may degenerate at u=0u=0 (in the case of φ′(0)=0φ′(0)=0). We consider the case of u0∈L∞(R)u0∈L∞(R), 0⩽u0(x)⩽10⩽u0(x)⩽1 a.e. x∈Rx∈R and the special case of ψ(u)=u−φ(u)ψ(u)=u−φ(u). We prove that the solution approaches the travelling wave solution (with speed c=1c=1), spreading either to the right or to the left, or to the two travelling waves moving in opposite directions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
J.I. Díaz, S. Kamin,