TY - JOUR
T1 - Asymptotic behavior of global classical solutions of quasilinear hyperbolic systems
AU - Kong, De-Xing
AU - Yang, Tong
PY - 2003
Y1 - 2003
N2 - We study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with weakly linearly degenerate characteristic fields. Based on the existence results on the global classical solution, we prove that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions at algebraic rate (1 + t)-μ, provided that the initial data decay at the rate (1 + |x|)-(1+μ) as x tends to ±∞, where μ, is a positive constant.
AB - We study the asymptotic behavior of global classical solutions of the Cauchy problem for general quasilinear hyperbolic systems with weakly linearly degenerate characteristic fields. Based on the existence results on the global classical solution, we prove that, when t tends to infinity, the solution approaches a combination of C1 travelling wave solutions at algebraic rate (1 + t)-μ, provided that the initial data decay at the rate (1 + |x|)-(1+μ) as x tends to ±∞, where μ, is a positive constant.
KW - Global classical solution
KW - Normalized coordinates
KW - Quasilinear hyperbolic system
KW - Travelling wave
KW - Weak linear degeneracy
UR - http://www.scopus.com/inward/record.url?scp=0037704901&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0037704901&origin=recordpage
U2 - 10.1081/PDE-120021192
DO - 10.1081/PDE-120021192
M3 - RGC 21 - Publication in refereed journal
SN - 0360-5302
VL - 28
SP - 1203
EP - 1220
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 5-6
ER -