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Asymptotic behaviour for a diffusion-convection equation with rapidly decreasing initial data. (English) Zbl 0954.35088
The large-time behaviour of solutions of the equation \(u_t-(u^m)_x=u_xx\), \(m>1\) with homogeneous Neumann boundary condition and bounded initial data is studied. The competition between the diffusion and the convection terms with respect to the concentration of the initial data is investigated. Convergence results are proved rescaling the equation and using Bernstein-type methods.
Reviewer: S.Tersian (Russe)
MSC:
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
35K65 Degenerate parabolic equations
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