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Weakly Singular Waves and Blow-up for a Regularization of the Shallow-water System
This thesis studies a regularization of the classical Saint-Venant (shallow-water) system, namely the regularized shallow-water (Airy or Saint-Venant) system, recentlyintroduced by D. Clamond and D. Dutykh. This regularization is non-dispersive and formally conserves mass, momentum and energy. We show that for every classical shock wave, this system admits a correspondingnon-oscillatory traveling wave solution which is continuous and piecewise smooth, having a weak singularity at a single pointdoi:10.1184/r1/7189049 fatcat:ifdodpj7b5dlfgpi45uum7popy