Artificial Shock Velocities Without Strong Traces

Develop a mathematically appropriate construction of artificial shock velocities for bounded entropy solutions of one-dimensional hyperbolic conservation laws that do not satisfy the Strong Trace Property, in order to recover a form of stability.

Background

The aa-contraction-with-shifts method introduces artificial velocities along shock curves to establish stability. The paper explains that the Strong Trace Property is used in constructing and analyzing these shift functions.

When strong traces are unavailable, the appropriate definition and analysis of such artificial velocities are not known, leaving open whether the stability method can be extended to broader classes of solutions.

References

Without the Strong Trace Property, it is unknown how to properly introduce artificial velocities at shocks in order to maintain some form of stability.

— The computational ansatz for convex integration of hyperbolic systems and a resolution of the Strong Trace Conjecture  (2609.09353 - Krupa, 8 Sep 2026) in Section 1, subsection “Strong Trace Property”

It is unknown if these different trace conditions suffice for the $a$-contraction theory.

— The computational ansatz for convex integration of hyperbolic systems and a resolution of the Strong Trace Conjecture  (2609.09353 - Krupa, 8 Sep 2026) in Section 1, subsection “Further questions on rank-one geometry,” subsubsection “Open questions”