On the existence, uniqueness and stability of entropy solutions to scalar conservation laws

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Golovaty, Dmitry¹  Truyen Nguyen¹ 

[1] Univ Akron, Dept Math, Akron, OH 44325 USA

关键词: Scalar conservation law;    Entropy solution;    Contraction principle;    Existence and uniqueness;    Continuous dependence;   

DOI  :  10.1016/j.jde.2012.04.024

来源: Elsevier

【 摘 要 】

We consider one-dimensional scalar conservation laws with and without viscosity where the flux function F (x, t, u) is only assumed to be absolutely continuous in x, locally integrable in t and continuous in u. The existence and uniqueness of entropy solutions for the associated initial-value problem are obtained through the vanishing viscosity method and the doubling variables technique. We also prove the stability of entropy solutions in C(inverted right perpendicular0, Tinverted left perpendicular; L-loc(1)(R)) and in C(inverted right perpendicular0, Tinverted left perpendicular; L-1(R)) with respect to both initial data and flux functions. Published by Elsevier Inc.

【 授权许可】

Free