Abstract. We generalize procedure from [28] on the case of more general triangular system of conservation laws arising from so called generalized pressureless gas dynamics. Using the weak asymptotic method [10,12], more precisely nonlinear superposition law [8], we approximate the nonlinear system by a linear one. Then, we can use usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how delta shock wave naturally arises along the characteristics.
Given a finite morphism ϕ : Y → X of quasi-smooth Berkovich curves over a complete, non-archimedean, nontrivially valued algebraically closed field k of characteristic 0, we prove a Riemann-Hurwitz formula relating their Euler-Poincaré characteristics (calculated using De Rham cohomology of their overconvergent structure sheaf). The main tools are padic Runge's theorem together with valuation polygons of analytic functions. Using the results obtained, we provide another point of view on Riemann-Hurwitz formula for finite morphisms of curves over algebraically closed fields of positive characteristic.
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