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A non-trivial conservation law with a trivial characteristic

Analysis of PDEs 2026-03-16 v1 Mathematical Physics Differential Geometry math.MP

Authors: Kostya Druzhkov

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Abstract

We show that the conservation law of the overdetermined system $u_t - 4u_x^3 - u_{xxx} = 0$ , $u_y = 0$ , associated with the characteristic $(u_{xy}, 0)$ , is non-trivial despite the characteristic vanishing on the system.

Keywords

conservation law overdetermined system characteristic non-trivial conservation

Cite

@article{arxiv.2502.11502,
  title  = {A non-trivial conservation law with a trivial characteristic},
  author = {Kostya Druzhkov},
  journal= {arXiv preprint arXiv:2502.11502},
  year   = {2026}
}

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16 pages