Annales Henri Poincaré, ISSN 1424-0637, 7/2019, Volume 20, Issue 7, pp. 2173 - 2270

We derive a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation consists of a coupled system of...

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | 35Q35 | Secondary 35L10 | Quantum Physics | 35Q75 | Dynamical Systems and Ergodic Theory | 35L67 | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS | Shock | Mathematics - Analysis of PDEs

Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | 35Q35 | Secondary 35L10 | Quantum Physics | 35Q75 | Dynamical Systems and Ergodic Theory | 35L67 | Classical and Quantum Gravitation, Relativity Theory | Physics | Elementary Particles, Quantum Field Theory | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PHYSICS, PARTICLES & FIELDS | Shock | Mathematics - Analysis of PDEs

Journal Article

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Full Text
Existence of global L∞ solutions to a generalized n × n hyperbolic system of LeRoux type

Acta Mathematica Scientia, ISSN 0252-9602, 05/2018, Volume 38, Issue 3, pp. 889 - 897

In this article, we give the existence of global bounded entropy solutions to the Cauchy problem of a generalized hyperbolic system of LeRoux type. The main...

Conservation laws | compensated compactness | viscosity method | 35L60 | LeRoux type | 35L67 | hyperbolic system | 35L65

Conservation laws | compensated compactness | viscosity method | 35L60 | LeRoux type | 35L67 | hyperbolic system | 35L65

Journal Article

Communications in Partial Differential Equations, ISSN 0360-5302, 08/2018, Volume 43, Issue 8, pp. 1242 - 1280

The paper studies the possible blowup of the total variation for entropy weak solutions of the p-system, modeling isentropic gas dynamics. It is assumed that...

hyperbolic conservation laws | Bounded variation | isentropic gas dynamics | 35B44 | 35L65(35B35 | 35L67 | rarefaction decay estimate | MATHEMATICS | MATHEMATICS, APPLIED | L-INFINITY | NONLINEAR HYPERBOLIC SYSTEMS | STABILITY | Gas dynamics | Rarefaction

hyperbolic conservation laws | Bounded variation | isentropic gas dynamics | 35B44 | 35L65(35B35 | 35L67 | rarefaction decay estimate | MATHEMATICS | MATHEMATICS, APPLIED | L-INFINITY | NONLINEAR HYPERBOLIC SYSTEMS | STABILITY | Gas dynamics | Rarefaction

Journal Article

Chinese Annals of Mathematics, Series B, ISSN 0252-9599, 11/2019, Volume 40, Issue 6, pp. 843 - 868

In this paper, the authors study the piston problem for the unsteady two-dimensional Euler system for a Chaplygin gas. The angle of the piston is allowed to...

Receding | Multi-Dimensional piston problem | 76L05 | Mathematics, general | Mathematics | Applications of Mathematics | Proceeding | 35L67 | 35L65 | 76N10 | Mach number

Receding | Multi-Dimensional piston problem | 76L05 | Mathematics, general | Mathematics | Applications of Mathematics | Proceeding | 35L67 | 35L65 | 76N10 | Mach number

Journal Article

Applicable Analysis, ISSN 0003-6811, 11/2019, Volume 98, Issue 15, pp. 2668 - 2687

The Riemann problem for the isentropic Euler system with the state equation for the extended Chaplygin gas is considered, and the Riemann solutions are...

76N15 | Riemann problem | Extended Chaplygin gas | delta shock wave | isentropic Euler system | 35L67 | Chaplygin gas | 35L65 | Shock waves | Equations of state

76N15 | Riemann problem | Extended Chaplygin gas | delta shock wave | isentropic Euler system | 35L67 | Chaplygin gas | 35L65 | Shock waves | Equations of state

Journal Article

Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 07/2019, Volume 22, Issue 5, pp. 773 - 785

In this paper, we use secant hyperbolic ansatz with tanh-coth method, combined with Riccati equation to derive complex travelling wave solutions to the...

Solitary wave | KdVB equation | Shock Waves | KdV equation | Secant hyperbolic ansatz | 35Q53 | 37K40 | 34K13 | 35L67 | Riccati equation | Tangent hyperbolic method

Solitary wave | KdVB equation | Shock Waves | KdV equation | Secant hyperbolic ansatz | 35Q53 | 37K40 | 34K13 | 35L67 | Riccati equation | Tangent hyperbolic method

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 10/2019, Volume 70, Issue 5, pp. 1 - 15

We address the Riemann problem for the one-dimensional compressive flow of a van der Waals gas, in which the external force is a given continuous function of...

Engineering | Compressible fluid | Mathematical Methods in Physics | Riemann problem | System of balance laws | Theoretical and Applied Mechanics | 35L67 | 35L65 | SYSTEM | MATHEMATICS, APPLIED | ENERGY | MOMENTUM | MASS | CONSERVATION-LAWS | EULER EQUATIONS

Engineering | Compressible fluid | Mathematical Methods in Physics | Riemann problem | System of balance laws | Theoretical and Applied Mechanics | 35L67 | 35L65 | SYSTEM | MATHEMATICS, APPLIED | ENERGY | MOMENTUM | MASS | CONSERVATION-LAWS | EULER EQUATIONS

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 10/2018, Volume 214, Issue 1, pp. 1 - 169

We study the Cauchy problem for the compressible Euler equations in two spatial dimensions under any physical barotropic equation of state except that of a...

Mathematics, general | Mathematics | 35Q31 | Primary 35L67 | 76N10 | Secondary 35L05 | MATHEMATICS | BLOWUP | SPACE DIMENSIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | SINGULARITIES | LINEAR WAVE-EQUATIONS | Wave propagation | Acoustic properties | Construction | Sound waves | Compressibility | Differential geometry | Acoustic propagation | Eulers equations | Euler-Lagrange equation | Cauchy problem | Operators (mathematics) | Sound propagation | Equations of state | Mathematical analysis | Vorticity | Differential equations | Plane waves | Chaplygin gas | Symmetry | Cartesian coordinates

Mathematics, general | Mathematics | 35Q31 | Primary 35L67 | 76N10 | Secondary 35L05 | MATHEMATICS | BLOWUP | SPACE DIMENSIONS | PARTIAL-DIFFERENTIAL-EQUATIONS | SINGULARITIES | LINEAR WAVE-EQUATIONS | Wave propagation | Acoustic properties | Construction | Sound waves | Compressibility | Differential geometry | Acoustic propagation | Eulers equations | Euler-Lagrange equation | Cauchy problem | Operators (mathematics) | Sound propagation | Equations of state | Mathematical analysis | Vorticity | Differential equations | Plane waves | Chaplygin gas | Symmetry | Cartesian coordinates

Journal Article

Archive for Rational Mechanics and Analysis, ISSN 0003-9527, 7/2019, Volume 233, Issue 1, pp. 87 - 166

We establish the interior and exterior Gauss–Green formulas for divergence-measure fields in L p over general open sets, motivated by the rigorous mathematical...

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EQUATIONS | MATHEMATICS, APPLIED | MECHANICS | Divergence | Deformation | Singularities | Mathematical analysis | Radon | Continuum mechanics | Formability | Product development | Fluxes | Boundaries | Representations

Physics, general | Fluid- and Aerodynamics | Theoretical, Mathematical and Computational Physics | Complex Systems | Physics | Classical Mechanics | EQUATIONS | MATHEMATICS, APPLIED | MECHANICS | Divergence | Deformation | Singularities | Mathematical analysis | Radon | Continuum mechanics | Formability | Product development | Fluxes | Boundaries | Representations

Journal Article

Acta Mathematica Scientia, ISSN 0252-9602, 01/2018, Volume 38, Issue 1, pp. 203 - 219

We study the singular structure of a family of two dimensional non-self-similar global solutions and their interactions for quasilinear hyperbolic conservation...

elementary wave | singular structure | quasilinear hyperbolic equations | global solutions | 35L67 | 35L65 | MATHEMATICS | DIMENSIONS | SPACE VARIABLES | CONVERGENCE | RIEMANN PROBLEM

elementary wave | singular structure | quasilinear hyperbolic equations | global solutions | 35L67 | 35L65 | MATHEMATICS | DIMENSIONS | SPACE VARIABLES | CONVERGENCE | RIEMANN PROBLEM

Journal Article

Numerische Mathematik, ISSN 0029-599X, 8/2018, Volume 139, Issue 4, pp. 867 - 912

The solution of the wave equation in a polyhedral domain in $${\mathbb {R}}^3$$ R3 admits an asymptotic singular expansion in a neighborhood of the corners and...

65M15 | 65M38 | Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 76Q05 | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 35L67 | DYNAMIC CONTACT PROBLEMS | MATHEMATICS, APPLIED | TIME | FINITE-ELEMENTS | Analysis | Numerical analysis

65M15 | 65M38 | Mathematical Methods in Physics | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Mathematical and Computational Engineering | 76Q05 | Mathematics, general | Mathematics | Numerical and Computational Physics, Simulation | 35L67 | DYNAMIC CONTACT PROBLEMS | MATHEMATICS, APPLIED | TIME | FINITE-ELEMENTS | Analysis | Numerical analysis

Journal Article

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, 06/2019, Volume 99, Issue 6, pp. e201800250 - n/a

In this paper we analyze the effects of a one‐way valve on the isothermal gas flow through a pipe. The valve keeps the flow at a constant value q∗>0, if...

gas flow | 76B75 | Riemann problem | systems of conservation laws | chattering | coupling conditions | valve | 35L67 | 35L65 | MATHEMATICS, APPLIED | MECHANICS | MODELS | POINT CONSTRAINTS | FLOW | GAS NETWORKS | Valves | Reaction time | Gas flow | Riemann solver | Coherence

gas flow | 76B75 | Riemann problem | systems of conservation laws | chattering | coupling conditions | valve | 35L67 | 35L65 | MATHEMATICS, APPLIED | MECHANICS | MODELS | POINT CONSTRAINTS | FLOW | GAS NETWORKS | Valves | Reaction time | Gas flow | Riemann solver | Coherence

Journal Article

SYMMETRY-BASEL, ISSN 2073-8994, 04/2019, Volume 11, Issue 4, p. 458

Blast waves are generated when an area grows abruptly with a supersonic speed, as in explosions. This problem is quite interesting, as a large amount of energy...

Rankine-Hugoniot conditions | blast waves | MULTIDISCIPLINARY SCIENCES | non-ideal gas | magnetogasdynamics | 35L67 | 58J45 | SHOCK-WAVES | MATHEMATICAL-THEORY | Rankine–Hugoniot conditions

Rankine-Hugoniot conditions | blast waves | MULTIDISCIPLINARY SCIENCES | non-ideal gas | magnetogasdynamics | 35L67 | 58J45 | SHOCK-WAVES | MATHEMATICAL-THEORY | Rankine–Hugoniot conditions

Journal Article

ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, 06/2016, Volume 96, Issue 6, pp. 681 - 695

The Riemann solutions for the one‐dimensional Chaplygin gas equations with a Coulomb‐like friction term are constructed explicitly. It is shown that the delta...

Riemann problem | Chaplygin gas equations | delta shock wave | Coulomb‐like friction term | 35B30 | 35L67 | 35L65 | 76N10 | Delta shock wave | Coulomb-like friction term | MATHEMATICS, APPLIED | DELTA-SHOCK-WAVES | SINGULARITIES | DARK ENERGY | MECHANICS | VANISHING PRESSURE LIMIT | VACUUM STATES | DYNAMICS | SYSTEMS | PROPAGATION | Deltas | Shock waves | Construction | Wave propagation | Friction | Mathematical analysis | Transportation | Chaplygin gas

Riemann problem | Chaplygin gas equations | delta shock wave | Coulomb‐like friction term | 35B30 | 35L67 | 35L65 | 76N10 | Delta shock wave | Coulomb-like friction term | MATHEMATICS, APPLIED | DELTA-SHOCK-WAVES | SINGULARITIES | DARK ENERGY | MECHANICS | VANISHING PRESSURE LIMIT | VACUUM STATES | DYNAMICS | SYSTEMS | PROPAGATION | Deltas | Shock waves | Construction | Wave propagation | Friction | Mathematical analysis | Transportation | Chaplygin gas

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 4/2019, Volume 79, Issue 1, pp. 249 - 272

In this work, a novel artificial viscosity method is proposed using smooth and compactly supported viscosities. These are derived by revisiting the widely used...

Computational Mathematics and Numerical Analysis | Discontinuous Galerkin methods | 65N35 | Shock capturing | Theoretical, Mathematical and Computational Physics | Mathematics | Artificial viscosity | Euler equations | 35L67 | 35L65 | Hyperbolic conservation laws | Algorithms | Mathematical and Computational Engineering | 35D40 | 65N30 | MATHEMATICS, APPLIED | Environmental law | Analysis | Methods | Mathematics - Numerical Analysis

Computational Mathematics and Numerical Analysis | Discontinuous Galerkin methods | 65N35 | Shock capturing | Theoretical, Mathematical and Computational Physics | Mathematics | Artificial viscosity | Euler equations | 35L67 | 35L65 | Hyperbolic conservation laws | Algorithms | Mathematical and Computational Engineering | 35D40 | 65N30 | MATHEMATICS, APPLIED | Environmental law | Analysis | Methods | Mathematics - Numerical Analysis

Journal Article

Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, 12/2019, Volume 21, Issue 4, pp. 1 - 9

The compressible Euler equations are the classical model in fluid dynamics. In this study, we investigate the life span of the projected 2-dimensional...

Fluid- and Aerodynamics | Initial value problem | 35B44 | Functional method | 35Q31 | Blowup | 35L67 | Physics | Rotational solutions | Mathematical Methods in Physics | Non-vacuum | Classical and Continuum Physics | Compressible Euler equations | 35B30 | 76U05

Fluid- and Aerodynamics | Initial value problem | 35B44 | Functional method | 35Q31 | Blowup | 35L67 | Physics | Rotational solutions | Mathematical Methods in Physics | Non-vacuum | Classical and Continuum Physics | Compressible Euler equations | 35B30 | 76U05

Journal Article

JOURNAL OF SCIENTIFIC COMPUTING, ISSN 0885-7474, 08/2019, Volume 80, Issue 2, pp. 924 - 956

This work is devoted to the derivation of an energy estimate to be satisfied by numerical schemes when approximating the weak solutions of the shallow water...

Well-balanced schemes | Godunov-type schemes | MATHEMATICS, APPLIED | Balance laws | APPROXIMATION | 65N08 | WELL-BALANCED SCHEME | MODEL | 35L67 | FINITE-VOLUME METHODS | 35L65 | SHALLOW-WATER EQUATIONS | Hyperbolic conservation laws | NUMERICAL VISCOSITY | Discrete entropy inequalities | SYSTEMS | FLOWS | HYPERBOLIC CONSERVATION-LAWS | EULER EQUATIONS | Environmental law | Analysis | Numerical Analysis | Analysis of PDEs | Mathematics

Well-balanced schemes | Godunov-type schemes | MATHEMATICS, APPLIED | Balance laws | APPROXIMATION | 65N08 | WELL-BALANCED SCHEME | MODEL | 35L67 | FINITE-VOLUME METHODS | 35L65 | SHALLOW-WATER EQUATIONS | Hyperbolic conservation laws | NUMERICAL VISCOSITY | Discrete entropy inequalities | SYSTEMS | FLOWS | HYPERBOLIC CONSERVATION-LAWS | EULER EQUATIONS | Environmental law | Analysis | Numerical Analysis | Analysis of PDEs | Mathematics

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 08/2016, Volume 57, Issue 8, p. 81506

An influential result of F. John states that no genuinely non-linear strictly hyperbolic quasi-linear first order system of partial differential equations in...

Lower bounds | Flux density | Partial differential equations | Upper bounds | Linearity | Crystals | Differential equations | Plane waves | Nonlinearity | Order quantity | Magnetic properties

Lower bounds | Flux density | Partial differential equations | Upper bounds | Linearity | Crystals | Differential equations | Plane waves | Nonlinearity | Order quantity | Magnetic properties

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2017, Volume 68, Issue 1, pp. 1 - 8

In this paper, we extend the finite propagation speed property for the compressible Euler equations with damping from the three-dimensional case to the general...

Damping | Finite propagation speed | 35B44 | 35Q31 | Radial symmetry | Blowup | Euler equations | Theoretical and Applied Mechanics | 35L67 | Compressible | Engineering | Mathematical Methods in Physics | 35B30

Damping | Finite propagation speed | 35B44 | 35Q31 | Radial symmetry | Blowup | Euler equations | Theoretical and Applied Mechanics | 35L67 | Compressible | Engineering | Mathematical Methods in Physics | 35B30

Journal Article

Duke Mathematical Journal, ISSN 0012-7094, 12/2012, Volume 161, Issue 15, pp. 2837 - 2908

We consider the 1-dimensional semilinear wave equation with power nonlinearity. We consider an arbitrary blowup solution u(x, t), the graph x bar right arrow...

EXISTENCE | MATHEMATICS | PROFILE | PARABOLIC EQUATIONS | HEAT-EQUATIONS | REGULARITY | BEHAVIOR | CURVE | UP SET | SURFACES | Analysis of PDEs | Mathematics | 35L05 | 35L71 | 35B40 | 35L67 | 35B44

EXISTENCE | MATHEMATICS | PROFILE | PARABOLIC EQUATIONS | HEAT-EQUATIONS | REGULARITY | BEHAVIOR | CURVE | UP SET | SURFACES | Analysis of PDEs | Mathematics | 35L05 | 35L71 | 35B40 | 35L67 | 35B44

Journal Article

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