# Linearly Degenerate Reducible Systems of Hydrodynamic Type

@article{Agafonov1998LinearlyDR, title={Linearly Degenerate Reducible Systems of Hydrodynamic Type}, author={Sergey I. Agafonov}, journal={Journal of Mathematical Analysis and Applications}, year={1998}, volume={222}, pages={15-37} }

Abstract We propose a complete description and classification of 3 × 3 linearly degenerate reducible systems of hydrodynamic type and show that any strictly hyperbolic system of this class can be reduced to the scalar Monge–Ampere type equation of the 3 d order.

## 13 Citations

Systems of conservation laws in the setting of the projective theory of congruences: reducible and linearly degenerate systems

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- 2002

Systems of conservation laws of Temple class, equations of associativity and linear¶congruences in P4

- Mathematics
- 2001

Abstract: We propose a geometric correspondence between (a) linearly degenerate systems of conservation laws with rectilinear rarefaction curves and (b) congruences of lines in projective space whose…

Frobenius 3-Folds via Singular Flat 3-Webs

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- 2012

We give a geometric interpretation of weighted homogeneous solutions to the associativity equation in terms of the web theory and construct a massive Frobenius 3-fold germ via a singular 3-web germ…

Systems of conservation laws of Temple class, equations of associativity and linear congruences in projective space

- Mathematics
- 2001

We propose a geometric correspondence between (a) linearly degenerate systems of conservation laws with rectilinear rarefaction curves and (b) congruences of lines in projective space whose…

Note on generic singularities of planar flat 3-webs

- Mathematics
- 2016

We propose a definition of genericity for singular flat planar 3-webs formed by integral curves of implicit ODEs and give a classification of generic singularities of such webs.

Duality for systems of conservation laws

- MathematicsLetters in Mathematical Physics
- 2019

For one-dimensional systems of conservation laws admitting two additional conservation laws, we assign a ruled hypersurface of codimension two in projective space. We call two such systems dual if…

J un 2 00 1 Systems of conservation laws of Temple class , equations of associativity and linear congruences in P 4

- Mathematics
- 2001

We propose a geometric correspondence between (a) linearly degenerate systems of conservation laws with rectilinear rarefaction curves and (b) congruences of lines in projective space whose…

A ug 2 01 9 Duality for systems of conservation laws

- Mathematics
- 2019

For one-dimensional systems of conservation laws admitting two additional conservation laws we assign a ruled surface of codimension two in projective space. We call two such systems dual if the…

Towards the classification of homogeneous third-order Hamiltonian operators

- Mathematics
- 2015

Let $V$ be a vector space of dimension $n+1$. We demonstrate that $n$-component third-order Hamiltonian operators of differential-geometric type are parametrised by the algebraic variety of elements…

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