Application of the Method of Differential Constraints to Systems of Equations Written in Riemann Invariants

2021 ◽  
Vol 62 (3) ◽  
pp. 5-14
Author(s):  
S. V. Meleshko ◽  
E. Shul'tz
Keyword(s):  
Systems Of Equations ◽  
Riemann Invariants ◽  
Differential Constraints ◽  
Method Of Differential Constraints

A differential constraints approach to partial invariance

1995 ◽  
Vol 6 (6) ◽  
pp. 631-637 ◽  
Author(s):  
Jeffrey Ondich
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Invariant Solutions ◽  
Differential Constraints ◽  
Partially Invariant Solutions ◽  
Prandtl Equations ◽  
Partial Invariance ◽  
Special Case ◽  
Method Of Differential Constraints

Ovsiannikov's method of partially invariant solutions of differential equations can be considered to be a special case of the method of differential constraints introduced by Yanenko and by Olver and Rosenau. Differential constraints are used to construct non-reducible partially invariant solutions of the boundary layer or Prandtl equations.

Method of Differential Constraints

2021 ◽  
pp. 303-352
Author(s):  
Andrei D. Polyanin ◽  
Alexei I. Zhurov
Keyword(s):  
Differential Constraints ◽  
Method Of Differential Constraints

scholarly journals Sufficient conditions for hyperbolicity and consistency of the dynamic equations for fluid-saturated solids

2021 ◽  
Author(s):  
Vladimir A. Osinov
Keyword(s):  
Boundary Value Problem ◽  
Wave Speed ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Positive Definiteness ◽  
Dynamic Equations ◽  
Necessary Condition ◽  
Systems Of Equations ◽  
Acoustic Tensor ◽  
Ill Posed

AbstractPrevious studies showed that the dynamic equations for a porous fluid-saturated solid may lose hyperbolicity and thus render the boundary-value problem ill-posed while the equations for the same but dry solid remain hyperbolic. This paper presents sufficient conditions for hyperbolicity in both dry and saturated states. Fluid-saturated solids are described by two different systems of equations depending on whether the permeability is zero or nonzero (locally undrained and drained conditions, respectively). The paper also introduces a notion of wave speed consistency between the two systems as a necessary condition which must be satisfied in order for the solution in the locally drained case to tend to the undrained solution as the permeability tends to zero. It is shown that the symmetry and positive definiteness of the acoustic tensor of the skeleton guarantee both hyperbolicity and the wave speed consistency of the equations.

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