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arXiv · 2502.02111

Explicit solution for the hyperbolic homogeneous scalar one-dimensional conservation law

Didier Clamond
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Abstract

A complex integral formula provides an explicit solution of the initial value problem for the nonlinear scala 1D equation $u_t+[f(u)]_x = 0$, for any flux $f(u)$ and initial condition $u_0(x)$ that are analytic. This formula is valid at least as long as $u$ remains analytic.

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Didier Clamond. 2025-02-04. Explicit solution for the hyperbolic homogeneous scalar one-dimensional conservation law. https://arxiv.org/abs/2502.02111

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