Mixed hyperbolic-elliptic systems in self-similar flows

DOI10.1007/BF01233673zbMath1043.35108MaRDI QIDQ4537487

Sunčica Čanić, Barbara Lee Keyfitz, Eun Heui Kim

Publication date: 4 September 2002

Published in: Boletim da Sociedade Brasileira de Matemática (Search for Journal in Brave)

zbMATH Keywords

nonlinear wave equationequations of mixed typecompressible gas dynamicstwo-dimensional Riemann problemsisentropic and adiabatic equations

Mathematics Subject Classification ID

Shocks and singularities for hyperbolic equations (35L67) PDEs in connection with fluid mechanics (35Q35) PDEs of mixed type (35M10) Hyperbolic conservation laws (35L65) Compressible fluids and gas dynamics (76N99)

Related Items (11)

The existence and uniqueness of a new boundary value problem (type of problem ``E) for linear system equations of the mixed hyperbolic-elliptic type in the multivariate dimension with the changing time direction ⋮ An Interaction of a Rarefaction Wave and a Transonic Shock for the Self-Similar Two-Dimensional Nonlinear Wave System ⋮ Two dimensional Riemann problems for the nonlinear wave system: rarefaction wave interactions ⋮ Diffraction of a shock into an expansion wavefront for the transonic self-similar nonlinear wave system in two space dimensions ⋮ The degenerate hyperbolic problem for the two‐dimensional nonlinear wave system ⋮ Discovery of PDEs driven by data with sharp gradient or discontinuity ⋮ Transonic shock and rarefaction wave interactions of two-dimensional Riemann problems for the self-similar nonlinear wave system ⋮ A global subsonic solution to an interacting transonic shock for the self-similar nonlinear wave equation ⋮ Numerical solutions to the self-similar transonic two-dimensional nonlinear wave system ⋮ TRANSONIC REGULAR REFLECTION FOR THE NONLINEAR WAVE SYSTEM ⋮ Classical solutions for the pressure-gradient equations in non-smooth and non-convex domains

Cites Work

• Quasi-one-dimensional Riemann problems and their role in self-similar two-dimensional problems
• On the 2-D Riemann problem for the compressible Euler equations I: Interaction of shocks and rarefaction waves
• Free boundary problems for the unsteady transonic small disturbance equation: Transonic regular reflection
• Flows of perfect fluids having two independent space-like variables. Reflection of a plane shock by a compressible wedge
• Conjecture on the Structure of Solutions of the Riemann Problem for Two-Dimensional Gas Dynamics Systems
• Numerical Solution of the Riemann Problem for Two-Dimensional Gas Dynamics
• A free boundary problem for a quasi-linear degenerate elliptic equation: Regular reflection of weak shocks
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