On the convergence rate of vanishing viscosity approximations

被引:43
作者
Bressan, A
Yang, T
机构
[1] SISSA, Dept Math, I-34014 Trieste, Italy
[2] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China
关键词
D O I
10.1002/cpa.20030
中图分类号
O29 [应用数学];
学科分类号
070104 [应用数学];
摘要
Given a strictly hyperbolic, genuinely nonlinear system of conservation laws, we prove the a priori bound parallel tou(t, (.)) - u(epsilon)(t, (.))parallel to(L1) = O(1)(1 + t) (.) rootepsilon \ln epsilon\ on the distance between an exact BV solution u and a viscous approximation u(epsilon), letting the viscosity coefficient epsilon --> 0. In the proof, starting from u we construct an approximation of the viscous solution u(epsilon) by taking a mollification u (*) psi(rootepsilon) and inserting viscous shock profiles at the locations of finitely many large shocks for each fixed epsilon. Error estimates are then obtained by introducing new Lyapunov functionals that control interactions of shock waves in the same family and also interactions of waves in different families. (C) 2004 Wiley Periodicals, Inc.
引用
收藏
页码:1075 / 1109
页数:35
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