Variational principle for multidimensional conservation laws and pressureless media

DOI10.1070/RM9918zbMath1439.35316WikidataQ114849639 ScholiaQ114849639MaRDI QIDQ5112441

Alexander I. Aptekarev, Yu. G. Rykov

Publication date: 29 May 2020

Published in: Russian Mathematical Surveys (Search for Journal in Brave)

zbMATH Keywords

quasilinear system

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (8)

On model two-dimensional pressureless gas flows: variational description and numerical algorithm based on adhesion dynamics ⋮ On the interaction of shock waves in two-dimensional isobaric media ⋮ Solutions with substance decay in pressureless gas dynamics systems ⋮ Dynamics of supports of extremal measures in the field of a point charge ⋮ Non-conventional and conventional solutions for one-dimensional pressureless gas ⋮ On the systems of conservation laws and on a new way to construct for them neural networks algorithms ⋮ Variational formulation of the problem of finding generalized solutions for quasilinear hyperbolic systems of conservation laws ⋮ Emergence of a hierarchy of singularities in zero-pressure media. Two-dimensional case

Cites Work

• On the variational representation of solutions to some quasilinear equations and systems of hyperbolic type on the basis of potential theory
• On the variational approach to systems of quasilinear conservation laws
• Direct and inverse problems for vector logarithmic potentials with external fields
• Detailed description of the evolution mechanism for singularities in the system of pressureless gas dynamics
• The Mhaskar–Saff Variational Principle and Location of the Shocks of Certain Hyperbolic Equations
• On Nikishin systems with discrete components and weak asymptotics of multiple orthogonal polynomials
• The Lax-Oleinik variational principle for some one-dimensional systems of quasilinear equations

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