The structure of MFD shock waves for rectilinear motion in some models of plasma

Hesaaraki, Mahmoud

doi:10.1090/s0002-9947-1995-1297528-4

Cited by 4 publications

(2 citation statements)

References 24 publications

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“…Let S(V , T ) be the entropy of the system. Following Conley and Smoller [5,6] and Hesaaraki [14,17], we consider a general form for thermodynamic state functions (instead of giving an specific expression) and we assume that the functions p(V , T ), e(V , T ), and S(V , T ) satisfy the following hypotheses.…”

Section: Hypotheses and Rest Pointsmentioning

confidence: 99%

“…Here we should mention that the elegant geometric technique, which was introduced by Conley and Smoller [5,6] and improved by Hesaaraki [14,17], cannot be applied here. This is because their proof relies heavily on the existence of a conic domain D in the plane, having the property that each point in D leaves it in a finite time.…”

Section: Remark Considering the Definition Ofmentioning

confidence: 99%

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Structure of shock waves in planar motion of plasma

Farjami¹,

Hesaaraki²

1998

Nonlinearity

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The mathematical question of the existence of structure for shock waves in planar motion of plasma is reduced to finding heteroclinic orbits of a system of five ordinary differential equations, which depend on five viscosity parameters. It is shown that the system is gradient-like and has four rest points. An explicit bound is obtained for the set of the bounded complete solutions, and an isolating neighbourhood for this system is constructed. Then using Conley theory we prove that the fast and slow shock waves, of arbitrary strength, always possess structure. Using a limiting technique, the switch-on and switch-off shock structures are obtained as a topological limit of the fast and slow shock structures, respectively. Furthermore, we show that most of the intermediate shocks, in the absence of the electric field, admit structure. The stability of all of these structures is also shown.

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Section: Hypotheses and Rest Pointsmentioning

confidence: 99%

Section: Remark Considering the Definition Ofmentioning

confidence: 99%

Structure of shock waves in planar motion of plasma

Farjami¹,

Hesaaraki²

1998

Nonlinearity

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On the Structure of MHD Shock Waves in Diffusive-Dispersive Media

Diehl

Rohde

2005

J. math. fluid mech.

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We consider the equations of compressible magnetohydrodynamics including the diffusive effects of fluid viscosity, thermal heat conductivity, electrical resistivity, and, in particular, the dispersive influence of the Hall term. The equations describe the dynamics of a plasma as it arises in astrophysical and technical applications.For a model problem we prove an existence result for shock profiles for all values of the Hall parameter. The same question for the complete six-dimensional system seems to be only solvable for small values of the Hall parameter, that is, viewing the Hall effect as a perturbation. To obtain substantial information on the complete system for all ranges of the dissipation parameters we present a careful numerical study. In particular the study confirms a well-known conjecture on the existence and bifurcation of orbits and illustrates the breaking of symmetry due to the Hall term. (2000). 76W05, 37M20. Mathematics Subject Classification

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