Displaying similar documents to “Anisotropic nonlinear diffusion with absorption: Existence and extinction.”

Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation

Shoshana Kamin, Philip Rosenau (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study the behaviour of the solutions of the Cauchy problem u t = u m x ⁢ x + u ⁢ 1 - u m - 1 , x ∈ R , t > 0 ⁢ u ⁢ 0 , x = u 0 ⁢ x , u 0 ⁢ x ≥ 0 , and prove that if initial data u 0 ⁢ x decay fast enough at infinity then the solution of the Cauchy problem approaches the travelling wave solution spreading either to the right or to the left, or two travelling waves moving in opposite directions. Certain generalizations are also mentioned.