TY - JOUR
T1 - Emergence of waves in a nonlinear convection-reaction-diffusion equation
AU - Kamin, Shoshana
AU - Rosenau, Philip
PY - 2004/8
Y1 - 2004/8
N2 - 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.
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
UR - http://www.scopus.com/inward/record.url?scp=4644348614&partnerID=8YFLogxK
U2 - 10.1515/ans-2004-0302
DO - 10.1515/ans-2004-0302
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:4644348614
SN - 1536-1365
VL - 4
SP - 251
EP - 272
JO - Advanced Nonlinear Studies
JF - Advanced Nonlinear Studies
IS - 3
ER -