Convergence Rate to the Nonlinear Waves for Viscous Conservation Laws on the Half Line

• Autores: Itsuko Hashimoto, Yoshihiro Ueda, Shuichi Kawashima
• Localización: Methods and applications of analysis, ISSN 1073-2772, Vol. 16, Nº 3, 2009, págs. 389-402
• Idioma: inglés
• DOI: 10.4310/maa.2009.v16.n3.a7
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• Resumen

  • We study the convergence rate of solutions to the initial-boundary value problem for scalar viscous conservation laws on the half line. Especially, we deal with the case where the Riemann problem for the corresponding hyperbolic equation admits transonic rarefaction waves. In this case, it is known that the solution tends toward a linear superposition of the stationary solution and the rarefaction wave. We show that the convergence rate is (1 + t).1 2 (1. 1 p ) log2(2 + t) in Lp norm (1  p < 1) and (1 + t).1 2+. in L1 norm if the initial perturbation from the corresponding superposition is located in H1 \ L1. The proof is given by a combination of the weighted Lp energy method and the L1 estimate.