Changes of type transitions for two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 × 2 Jordan block) on the transition line with hodograph equations becoming parabolic. Conditions which allow or forbid the transition from the hyperbolic domain to elliptic one are discussed. Hamiltonian systems and their special subclasses and equations, such as dispersionless nonlinear Schrdinger, dispersionless Boussinesq, one-dimensional isentropic gas dynamics equations, and nonlinear wave equations are studied. Numerical results concerning the crossing of transition line for the dispersionless Boussinesq equation are also presented.

Konopelchenko, B., Ortenzi, G. (2017). Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 50(21) [10.1088/1751-8121/aa6777].

Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems

ORTENZI, GIOVANNI
Ultimo
2017

Abstract

Changes of type transitions for two-component hydrodynamic type systems are discussed. It is shown that these systems generically assume the Jordan form (with 2 × 2 Jordan block) on the transition line with hodograph equations becoming parabolic. Conditions which allow or forbid the transition from the hyperbolic domain to elliptic one are discussed. Hamiltonian systems and their special subclasses and equations, such as dispersionless nonlinear Schrdinger, dispersionless Boussinesq, one-dimensional isentropic gas dynamics equations, and nonlinear wave equations are studied. Numerical results concerning the crossing of transition line for the dispersionless Boussinesq equation are also presented.
Articolo in rivista - Articolo scientifico
Hamiltonian hydrodynamic systems; hyperbolic-elliptic transition; parabolic systems;
Hamiltonian hydrodynamic systems; hyperbolic-elliptic transition; parabolic systems; Statistical and Nonlinear Physics; Statistics and Probability; Modeling and Simulation; Mathematical Physics; Physics and Astronomy (all)
English
2017
Konopelchenko, B., Ortenzi, G. (2017). Jordan form, parabolicity and other features of change of type transition for hydrodynamic type systems. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 50(21) [10.1088/1751-8121/aa6777].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/157875
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