Emergence of waves in a nonlinear convection-reaction-diffusion equation

Shoshana Kamin; Philip Rosenau

doi:10.1515/ans-2004-0302

Emergence of waves in a nonlinear convection-reaction-diffusion equation

Shoshana Kamin^*
, Philip Rosenau

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

In this work we prove that for some class of initial data the solution of the Cauchy problem u_t = (u^m)_xx + a(u ^m)_x + u(1 - u^m-1), x ∈ ℝ, t > 0 u(0, x) = u₀(x), u₀(x) ≥ 0 approaches the travelling solution, spreading either to the right or to the left, or two travelling waves moving in opposite directions.

Original language	English
Pages (from-to)	251-272
Number of pages	22
Journal	Advanced Nonlinear Studies
Volume	4
Issue number	3
DOIs	https://doi.org/10.1515/ans-2004-0302
State	Published - Aug 2004

Keywords

Asymptotic behaviour of solutions
Nonlinear diffusion
Travelling waves

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abstract = "In this work we prove that for some class of initial data the solution of the Cauchy problem ut = (um)xx + a(u m)x + u(1 - um-1), x ∈ ℝ, t > 0 u(0, x) = u0(x), u0(x) ≥ 0 approaches the travelling solution, spreading either to the right or to the left, or two travelling waves moving in opposite directions.",

keywords = "Asymptotic behaviour of solutions, Nonlinear diffusion, Travelling waves",

author = "Shoshana Kamin and Philip Rosenau",

year = "2004",

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AB - In this work we prove that for some class of initial data the solution of the Cauchy problem ut = (um)xx + a(u m)x + u(1 - um-1), x ∈ ℝ, t > 0 u(0, x) = u0(x), u0(x) ≥ 0 approaches the travelling solution, spreading either to the right or to the left, or two travelling waves moving in opposite directions.

KW - Asymptotic behaviour of solutions

KW - Nonlinear diffusion

KW - Travelling waves

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Emergence of waves in a nonlinear convection-reaction-diffusion equation

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