TY - JOUR
T1 - Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation
AU - Kamin, Shoshana
AU - Rosenau, Philip
PY - 2004
Y1 - 2004
N2 - We study the behaviour of the solutions of the Cauchy problem ut = (um)xx + u(1 - um-1), xεR, t > 0 u(0, x) = u0(x), u0(x) ≥ 0, and prove that if initial data u0(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.
AB - We study the behaviour of the solutions of the Cauchy problem ut = (um)xx + u(1 - um-1), xεR, t > 0 u(0, x) = u0(x), u0(x) ≥ 0, and prove that if initial data u0(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.
KW - Asymptotic behaviour of solutions
KW - Nonlinear diffusion
KW - Reaction-diffusion equation
KW - Travelling waves
UR - http://www.scopus.com/inward/record.url?scp=84887237521&partnerID=8YFLogxK
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AN - SCOPUS:84887237521
VL - 15
SP - 271
EP - 280
JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica E Applicazioni
SN - 1120-6330
IS - 3-4
ER -