publication . Article . 2016

Loss of hyperbolicity changes the number of wave groups in Riemann problems

Vítor Matos; Julio Daniel Silva; Dan Marchesin;
Open Access English
  • Published: 01 Jun 2016
  • Country: Portugal
Themain goal of ourwork is to showthat there exists a class of 2×2 Riemann problems for which the solution comprises a singlewave group for an open set of initial conditions. This wave group comprises a 1-rarefaction joined to a 2-rarefaction, not by an intermediate state, but by a doubly characteristic shock, 1-left and 2-right characteristic. In order to ensure that perturbations of initial conditions do not destroy the adjacency of the waves, local transversality between a composite curve foliation and a rarefaction curve foliation is necessary.
free text keywords: Equações diferenciais, Matemática, Differential equations, Mathematics, :Matemática [Ciências exactas e naturais], :Mathematics [Natural sciences], Riemann problem, symbols.namesake, symbols, Mathematical analysis, Adjacency list, Mathematics, Rarefaction (ecology), Structural stability, Transversality, Perturbation (astronomy), Riemann hypothesis, Open set
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