Abstract
Shock waves are nonlinear structures characterized by a discontinuous jump in the wave profile. There exist prototypical examples of partial differential equations (PDEs), including the well-known Burgers’ equation (without dissipation), where the relevant waveforms feature infinite derivatives arising in finite time. To study shock waves in equations like the inviscid Burgers’ equations one can study the evolution of Riemann initial conditions involving a jump in the initial data.
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Chong, C., Kevrekidis, P.G. (2018). Dispersive Shock Waves. In: Coherent Structures in Granular Crystals. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-77884-6_2
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DOI: https://doi.org/10.1007/978-3-319-77884-6_2
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