The initial discontinuity decay problem for shallow water equations on slopes

Abstract

The initial discontinuity decay problem for shallow water equations on slopes is formulated and solved. The nondegenerate transformation of dependent and independent variables that reduces the Saint–Venant equations on slopes to the classical shallow water equations on flat plates is used. The solution of a basic initial discontinuity decay problem for the classical equations of shallow water above a homogeneous surface is provided. The independent derivation of this solution here is directed first of all on mathematicians and physicists because, for one reason, it enables generalisations to more complicated geometries.