Hyperbolic balance laws with source terms allow non-unique entropy solutions. By taking the source term as a variable and stating its time derivative to be zero, a balance law can be rewritten in a quasi-linear form. This then reveals the loss of strict hyperbolicity at critical states, the so called resonance phenomenon. Numerical schemes are sensitive to this phenomenon and it is uncertain, which entropy solution (if it is non-unique) will be created by an appropriate numerical scheme.

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Last updated: 27 Feb 2024