Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4668761 | Bulletin des Sciences Mathématiques | 2014 | 22 Pages |
Abstract
We obtain the precise asymptotic (tââ) for solution f(x,t) of Cauchy-Gelfand problem for quasilinear conservation law âfât+Ï(f)âfâx=0 with initial data of bounded variation f(x,0)=f0(x). The main theorem develops results of Liu (1981) [22], Kruzhkov, Petrosjan (1987) [20], Henkin, Shananin (2004) [10], Henkin (2012) [9]. Proofs are based on vanishing viscosity estimates and localized Maxwell type conservation laws. The main application consists in the reconstruction of parameters of initial data responsible for location of inviscid shock waves in the solution f(x,t).
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
G.M. Henkin, A.A. Shananin,