Conservation Laws for Hyperbolic Equations: Search Algorithm for Local Preimage with Respect to the Total Derivative

2021 ◽  
Author(s):  
S. Ya. Startsev
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Equations ◽  
Search Algorithm ◽  
Total Derivative

scholarly journals Group Classification and Conservation Laws of a Class of Hyperbolic Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
J. C. Ndogmo
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Linear Dependence ◽  
Hyperbolic Equations ◽  
Group Classification ◽  
The Family ◽  
The Given ◽  
Low Order

Abstracts. A method for the group classification of differential equations is proposed. It is based on the determination of all possible cases of linear dependence of certain indeterminates appearing in the determining equations of symmetries of the equation. The method is simple and systematic and applied to a family of hyperbolic equations. Moreover, as the given family contains several known equations with important physical applications, low-order conservation laws of some relevant equations from the family are computed, and the results obtained are discussed with regard to the symmetry integrability of a particular class from the underlying family of hyperbolic equations.

scholarly journals Nonoscillatory Central Schemes for Hyperbolic Systems of Conservation Laws in Three-Space Dimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Andrew N. Guarendi ◽  
Abhilash J. Chandy
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Equations ◽  
Hyperbolic Systems ◽  
Scaling Analysis ◽  
Hyperbolic Conservation ◽  
Central Schemes ◽  
Systems Of Conservation Laws ◽  
Ideal Magnetohydrodynamic ◽  
Three Space

We extend a family of high-resolution, semidiscrete central schemes for hyperbolic systems of conservation laws to three-space dimensions. Details of the schemes, their implementation, and properties are presented together with results from several prototypical applications of hyperbolic conservation laws including a nonlinear scalar equation, the Euler equations of gas dynamics, and the ideal magnetohydrodynamic equations. Parallel scaling analysis and grid-independent results including contours and isosurfaces of density and velocity and magnetic field vectors are shown in this study, confirming the ability of these types of solvers to approximate the solutions of hyperbolic equations efficiently and accurately.

THE EQUATIONS OF ELASTICITY WITH DISSIPATION AS A NONTRIVIAL EXAMPLE OF THERMODYNAMICALLY CONSISTENT HYPERBOLIC EQUATIONS

2004 ◽  
Vol 01 (02) ◽  
pp. 235-249 ◽  
Author(s):  
SERGEI K. GODUNOV
Keyword(s):  
Conservation Laws ◽  
Hyperbolic System ◽  
Hyperbolic Equations ◽  
Symmetric Hyperbolic System ◽  
Initial Values ◽  
Elasticity Equations ◽  
Dissipative Terms ◽  
Galilean Invariant

A thermodynamically consistent Galilean-invariant formalization of the elasticity equations is proposed. The equations under consideration form a symmetric hyperbolic system but they are non-conservative. The conservation laws are valid only on a solution with special initial values. Difficulties arising while introducing the dissipative terms are briefly discussed.

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