Partial dissipation and sub-shock

Liu, Tai-Ping

doi:10.1090/qam/1657

Author: Tai-Ping Liu
Journal: Quart. Appl. Math. 81 (2023), 483-506
MSC (2020): Primary 35L65, 35L67; Secondary 76N10
DOI: https://doi.org/10.1090/qam/1657
Published electronically: March 6, 2023
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Abstract: To study the dissipation property of a physical system one first considers infinitesimal waves for the analysis of weakly nonlinear phenomena. For some physical systems, the dissipation is partial and there is the appearance of sub-shocks in a strong traveling trajectory. The phenomenon of partial dissipation can occur for systems of hyperbolic balance laws and also for viscous conservation laws in continuum physics. We illustrate the phenomenon for a simple relaxation model and for the Navier-Stokes equations for compressible media. The admissibility criteria and the formation of sub-shocks are studied through the zero viscosity limit.

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