5 problems

Consider a vacuum free-boundary problem with specific enthalpy $h$ and vacuum boundary $x=b(t)$. The physical vacuum condition is … In the case where the initial boundary behavior…

The one-dimensional Burgers equation admits finite-codimension stable shock formation under suitable initial-data conditions, as established by the preceding proposition. Finite-co…

Uniqueness and classification conjecture. The solution of the Riemann problem consisting of the governing equations and initial condition is unique for any given $\gamma$ and…

Consider a wide class of gas-dynamic models with conservative regularization, including the one-dimensional R-gas dynamics discussed here. A steady shock-like solution is a station…

The equations of compressible gas dynamics can form shocks, singularities across which the physical variables change discontinuously. A caustic is a singular structure formed by wa…