A new nonlinear functional for general scalar conservation laws

Zaihong Jiang Tong Yang

Analysis of PDEs mathscidoc:1912.431018

Journal of Differential Equations, 246, (11), 4284-4308, 2009.6
The approach based on the construction of some nonlinear functionals was proved to be robust in the study of the well-posedness theories of hyperbolic conservation laws, especially in one space dimensional case. In particular, a generalized entropy functional was constructed in [T.-P. Liu, T. Yang, A new entropy functional for scalar conservation laws, Comm. Pure Appl. Math. 52 (1999) 14271442] for the L 1 stability of weak solutions. However, this generalized functional is so far only defined for scalar equations with convex flux function. In this paper, we introduce a new nonlinear functional which is motivated by the new Glimm functional introduced in [J.-L. Hua, Z.-H. Jiang, T. Yang, A new Glimm functional and convergence rate of Glimm scheme for general systems of hyperbolic conservation laws, preprint] for general scalar conservation laws. This functional improves the one given in [H.-X. Liu, T. Yang, A
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  title={A new nonlinear functional for general scalar conservation laws},
  author={Zaihong Jiang, and Tong Yang},
  booktitle={Journal of Differential Equations},
Zaihong Jiang, and Tong Yang. A new nonlinear functional for general scalar conservation laws. 2009. Vol. 246. In Journal of Differential Equations. pp.4284-4308. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211239917856582.
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