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Asymptotic behavior of global classical solutions of quasilinear hyperbolic systems. (English) Zbl 1024.35068
Summary: 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 C 1 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.

35L60Nonlinear first-order hyperbolic equations
35L40First order hyperbolic systems, general
35L45First order hyperbolic systems, initial value problems
35B40Asymptotic behavior of solutions of PDE