2011, Graduate studies in mathematics, ISBN 0821853694, Volume 125, xviii, 236

Book

Computers and Mathematics with Applications, ISSN 0898-1221, 05/2016, Volume 71, Issue 10, pp. 1990 - 2000

We consider Riemann–Hilbert boundary value problems (for short RHBVPs) with variable coefficients for axially symmetric poly-monogenic functions, i.e.,...

Quaternion analysis | Iterated generalized Cauchy–Riemann operator | Variable coefficients | Axial symmetry | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Iterated generalized Cauchy-Riemann operator | Riemann-Hilbert problems | THEOREM | CLIFFORD ANALYSIS | Construction | Boundary value problems | Integrals | Mathematical analysis | Mathematical models | Representations | Cauchy-Riemann equations | Symmetry

Quaternion analysis | Iterated generalized Cauchy–Riemann operator | Variable coefficients | Axial symmetry | Riemann–Hilbert problems | MATHEMATICS, APPLIED | Iterated generalized Cauchy-Riemann operator | Riemann-Hilbert problems | THEOREM | CLIFFORD ANALYSIS | Construction | Boundary value problems | Integrals | Mathematical analysis | Mathematical models | Representations | Cauchy-Riemann equations | Symmetry

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2018, Volume 375, pp. 1238 - 1269

The Riemann problem, and the associated generalized Riemann problem, are increasingly seen as the important building blocks for modern higher order...

Hyperbolic conservation laws | Stiff sources | Generalized Riemann problem solver | Non-conservative hyperbolic problems | HLLI Riemann solver | DISCONTINUOUS GALERKIN SCHEMES | HYPERBOLIC SYSTEMS | ASYMPTOTIC-EXPANSION | EQUATIONS | IMPLEMENTATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EULERIAN GRP SCHEME | ADER SCHEMES | GODUNOV-TYPE METHODS | FINITE-VOLUME SCHEMES | PIECEWISE PARABOLIC METHOD | Environmental law | Mathematical problems | Energy dissipation | Conservation | Problem solving | Eigenvectors | Computational physics | Hyperbolic systems | Riemann solver | Eigen values | Mathematics - Numerical Analysis

Hyperbolic conservation laws | Stiff sources | Generalized Riemann problem solver | Non-conservative hyperbolic problems | HLLI Riemann solver | DISCONTINUOUS GALERKIN SCHEMES | HYPERBOLIC SYSTEMS | ASYMPTOTIC-EXPANSION | EQUATIONS | IMPLEMENTATION | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EULERIAN GRP SCHEME | ADER SCHEMES | GODUNOV-TYPE METHODS | FINITE-VOLUME SCHEMES | PIECEWISE PARABOLIC METHOD | Environmental law | Mathematical problems | Energy dissipation | Conservation | Problem solving | Eigenvectors | Computational physics | Hyperbolic systems | Riemann solver | Eigen values | Mathematics - Numerical Analysis

Journal Article

Results in Mathematics, ISSN 1422-6383, 6/2013, Volume 63, Issue 3, pp. 1375 - 1394

In this paper we consider a kind of Riemann boundary value problem (for short RBVP) for null solutions to the iterated generalized Cauchy–Riemann operator and...

Generalized Cauchy–Riemann operator | 30D10 | 32A25 | Clifford analysis | 58A10 | Poly-Cauchy type integral | Mathematics, general | 30G35 | Riemann boundary value problems | Mathematics | Generalized Cauchy-Riemann operator | MATHEMATICS | MATHEMATICS, APPLIED | DIRAC

Generalized Cauchy–Riemann operator | 30D10 | 32A25 | Clifford analysis | 58A10 | Poly-Cauchy type integral | Mathematics, general | 30G35 | Riemann boundary value problems | Mathematics | Generalized Cauchy-Riemann operator | MATHEMATICS | MATHEMATICS, APPLIED | DIRAC

Journal Article

ADVANCES IN APPLIED CLIFFORD ALGEBRAS, ISSN 0188-7009, 09/2017, Volume 27, Issue 3, pp. 2493 - 2508

In this paper we are interested in finding solutions to Riemann-Hilbert boundary value problems, for short Riemann-Hilbert problems, with variable coefficients...

SPACE | MATHEMATICS, APPLIED | Riemann-Hilbert problems | OPERATOR | equation Quaternion analysis | Generalized Cauchy-Riemann | BOUNDARY-VALUE-PROBLEMS | PHYSICS, MATHEMATICAL

SPACE | MATHEMATICS, APPLIED | Riemann-Hilbert problems | OPERATOR | equation Quaternion analysis | Generalized Cauchy-Riemann | BOUNDARY-VALUE-PROBLEMS | PHYSICS, MATHEMATICAL

Journal Article

力学学报：英文版, ISSN 0567-7718, 2015, Volume 31, Issue 2, pp. 153 - 161

In this paper,we propose a numerical method to estimate the unknown order of a Riemann-Liouville fractional derivative for a fractional Stokes＇ first problem...

广义二阶流体 | Levenberg-Marquardt算法 | 分数阶导数 | 加热 | 估计 | 黎曼 | 逆问题 | gamma函数 | Engineering | Computational Intelligence | Implicit numerical method | Riemann–Liouville fractional derivative | Engineering Fluid Dynamics | Generalized second grade fluid | Fractional sensitivity equation | Theoretical and Applied Mechanics | Classical Continuum Physics | Inverse problem | UNSTEADY-FLOW | MECHANICS | Riemann-Liouville fractional derivative | VISCOELASTIC FLUID | ENGINEERING, MECHANICAL | Models | Algorithms

广义二阶流体 | Levenberg-Marquardt算法 | 分数阶导数 | 加热 | 估计 | 黎曼 | 逆问题 | gamma函数 | Engineering | Computational Intelligence | Implicit numerical method | Riemann–Liouville fractional derivative | Engineering Fluid Dynamics | Generalized second grade fluid | Fractional sensitivity equation | Theoretical and Applied Mechanics | Classical Continuum Physics | Inverse problem | UNSTEADY-FLOW | MECHANICS | Riemann-Liouville fractional derivative | VISCOELASTIC FLUID | ENGINEERING, MECHANICAL | Models | Algorithms

Journal Article

2004, ISBN 0691119538, viii, 218

Book

International Journal of Non-Linear Mechanics, ISSN 0020-7462, 04/2019, Volume 110, pp. 16 - 20

This paper is devoted to obtain an exact solution to generalized Riemann problem for nonhomogeneous quasilinear hyperbolic system of partial differential...

Nonhomogeneous rate-type material | Differential constraint method | Generalized Riemann problem | Exact solution | DIFFERENTIAL-CONSTRAINTS | MECHANICS | EQUATIONS | SYSTEMS | Differential equations | Rarefaction | Partial differential equations | Mathematical analysis | Hyperbolic systems | Exact solutions

Nonhomogeneous rate-type material | Differential constraint method | Generalized Riemann problem | Exact solution | DIFFERENTIAL-CONSTRAINTS | MECHANICS | EQUATIONS | SYSTEMS | Differential equations | Rarefaction | Partial differential equations | Mathematical analysis | Hyperbolic systems | Exact solutions

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2013, Volume 403, Issue 2, pp. 434 - 450

The Riemann problem for one dimensional generalized Chaplygin gas dynamics is considered. Its two characteristic fields are genuinely nonlinear, but the...

Numerical simulations | Riemann problem | Generalized Rankine–Hugoniot conditions | Delta-shock wave | Generalized Chaplygin gas | Generalized Rankine-Hugoniot conditions | HYPERBOLIC-SYSTEMS | MATHEMATICS, APPLIED | VISCOSITY APPROACH | DELTA-SHOCK WAVES | ISENTROPIC EULER EQUATIONS | ENTROPY SOLUTIONS | MATHEMATICS | VANISHING PRESSURE LIMIT | VACUUM STATES | CONVERGENCE | LAX-FRIEDRICHS SCHEME | CONSERVATION-LAWS

Numerical simulations | Riemann problem | Generalized Rankine–Hugoniot conditions | Delta-shock wave | Generalized Chaplygin gas | Generalized Rankine-Hugoniot conditions | HYPERBOLIC-SYSTEMS | MATHEMATICS, APPLIED | VISCOSITY APPROACH | DELTA-SHOCK WAVES | ISENTROPIC EULER EQUATIONS | ENTROPY SOLUTIONS | MATHEMATICS | VANISHING PRESSURE LIMIT | VACUUM STATES | CONVERGENCE | LAX-FRIEDRICHS SCHEME | CONSERVATION-LAWS

Journal Article

Journal of Scientific Computing, ISSN 0885-7474, 11/2016, Volume 69, Issue 2, pp. 805 - 840

In a wide class of high order shock-capturing methods for hyperbolic conservation laws, the solution of the conservation law is represented at each time-step...

Hyperbolic conservation laws | Computational Mathematics and Numerical Analysis | Generalized Riemann problems | Algorithms | 65M08 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | ADER methods | Mathematics | 35L65 | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | RELATIVISTIC MAGNETOHYDRODYNAMICS | NAVIER-STOKES EQUATIONS | ADER SCHEMES | GODUNOV-TYPE METHODS | HYPERBOLIC BALANCE LAWS | CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Mechanical engineering | Environmental law

Hyperbolic conservation laws | Computational Mathematics and Numerical Analysis | Generalized Riemann problems | Algorithms | 65M08 | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | ADER methods | Mathematics | 35L65 | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | ESSENTIALLY NONOSCILLATORY SCHEMES | HIGH-ORDER | RELATIVISTIC MAGNETOHYDRODYNAMICS | NAVIER-STOKES EQUATIONS | ADER SCHEMES | GODUNOV-TYPE METHODS | HYPERBOLIC BALANCE LAWS | CONSERVATION-LAWS | FINITE-VOLUME SCHEMES | Mechanical engineering | Environmental law

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2019, Volume 472, Issue 1, pp. 1001 - 1027

We study an Eulerian droplet model which can be seen as the pressureless gas system with a source term, a subsystem of this model and the inviscid Burgers...

Delta-shock waves | Blowup | Eulerian particle model | Burgers equation | Generalized Rankine–Hugoniot conditions | Source term | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | EQUATIONS | CAUCHY-PROBLEM | VISCOSITY | SIMULATION | UNIQUENESS | MATHEMATICS | VANISHING PRESSURE LIMIT | VACUUM STATES | Generalized Rankine-Hugoniot conditions | CONSERVATION-LAWS | INITIAL DATA

Delta-shock waves | Blowup | Eulerian particle model | Burgers equation | Generalized Rankine–Hugoniot conditions | Source term | MATHEMATICS, APPLIED | HYPERBOLIC SYSTEMS | EQUATIONS | CAUCHY-PROBLEM | VISCOSITY | SIMULATION | UNIQUENESS | MATHEMATICS | VANISHING PRESSURE LIMIT | VACUUM STATES | Generalized Rankine-Hugoniot conditions | CONSERVATION-LAWS | INITIAL DATA

Journal Article

Mathematics, ISSN 2227-7390, 12/2018, Volume 6, Issue 12, p. 316

Riemann's method is one of the definitive ways of solving Cauchy's problem for a second order linear hyperbolic partial differential equation in two variables....

Hypergeometric function of several variables | Point symmetry | Generalized symmetry | Riemann function | Riemann's method | MATHEMATICS | SYMMETRY | INVERSE PROBLEM | EQUATIONS | hypergeometric function of several variables | point symmetry | OPERATORS | generalized symmetry | Riemann’s method

Hypergeometric function of several variables | Point symmetry | Generalized symmetry | Riemann function | Riemann's method | MATHEMATICS | SYMMETRY | INVERSE PROBLEM | EQUATIONS | hypergeometric function of several variables | point symmetry | OPERATORS | generalized symmetry | Riemann’s method

Journal Article

Integral Equations and Operator Theory, ISSN 0378-620X, 10/2014, Volume 80, Issue 2, pp. 239 - 264

We generalize the notion of $${\mathfrak{Q}}$$ Q -classes $${C_{{Q_1} {Q_2}}}$$ C Q 1 Q 2 , which was introduced in the context of Wiener–Hopf factorization,...

15A24 | matrix equations | Analysis | Secondary 47B35 | Mathematics | Primary 47A68 | Toeplitz operators | factorization | Riemann–Hilbert problems | MATHEMATICS | MEROMORPHIC FACTORIZATION | GENERALIZED FACTORIZATION | Riemann-Hilbert problems | DOUGLAS | EXPLICIT FACTORIZATION | EQUATIONS | KHRAPKOV MATRIX FUNCTIONS | RUDIN

15A24 | matrix equations | Analysis | Secondary 47B35 | Mathematics | Primary 47A68 | Toeplitz operators | factorization | Riemann–Hilbert problems | MATHEMATICS | MEROMORPHIC FACTORIZATION | GENERALIZED FACTORIZATION | Riemann-Hilbert problems | DOUGLAS | EXPLICIT FACTORIZATION | EQUATIONS | KHRAPKOV MATRIX FUNCTIONS | RUDIN

Journal Article

Computers and Fluids, ISSN 0045-7930, 06/2018, Volume 169, pp. 201 - 212

•A new solver for the GRP without an exact Riemann solver.•Turn any HLL-type Riemann solver into a GRP solver of any higher order.•No need to compute...

Hyperbolic conservation laws | Generalized Riemann problems | High order finite volume methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ASYMPTOTIC-EXPANSION | EQUATIONS | SYSTEMS | HIGH-ORDER | CONSERVATION-LAWS | COMPRESSIBLE FLUID-FLOWS | SCHEMES | Environmental law

Hyperbolic conservation laws | Generalized Riemann problems | High order finite volume methods | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ASYMPTOTIC-EXPANSION | EQUATIONS | SYSTEMS | HIGH-ORDER | CONSERVATION-LAWS | COMPRESSIBLE FLUID-FLOWS | SCHEMES | Environmental law

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 12/2015, Volume 303, pp. 146 - 172

We present a semi-analytical, implicit solution to the generalized Riemann problem (GRP) for non-linear systems of hyperbolic balance laws with stiff source...

Stiff source terms | Hyperbolic balance laws | Generalized Riemann problem | Cauchy–Kowalewskaya procedure | High-order ADER schemes | Cauchy-kowalewskaya procedure | Generalized riemann problem | DISCONTINUOUS GALERKIN SCHEMES | DIFFUSION-REACTION EQUATIONS | HIGH-ORDER | SOLVERS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | PNPM SCHEMES | SYSTEMS | Cauchy-Kowalewskaya procedure | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Glass fiber reinforced plastics | Nonlinear dynamics | Accuracy | Mathematical analysis | Solvers | Mathematical models | Dynamical systems | Convergence

Stiff source terms | Hyperbolic balance laws | Generalized Riemann problem | Cauchy–Kowalewskaya procedure | High-order ADER schemes | Cauchy-kowalewskaya procedure | Generalized riemann problem | DISCONTINUOUS GALERKIN SCHEMES | DIFFUSION-REACTION EQUATIONS | HIGH-ORDER | SOLVERS | PHYSICS, MATHEMATICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | ADER SCHEMES | PNPM SCHEMES | SYSTEMS | Cauchy-Kowalewskaya procedure | CONSERVATION-LAWS | UNSTRUCTURED MESHES | FINITE-VOLUME SCHEMES | Glass fiber reinforced plastics | Nonlinear dynamics | Accuracy | Mathematical analysis | Solvers | Mathematical models | Dynamical systems | Convergence

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 02/2014, Volume 259, pp. 358 - 389

The generalized Riemann problems (GRP) for nonlinear hyperbolic systems of balance laws in one space dimension are now well-known and can be formulated as...

GRP solver | Generalized Riemann problem | Generalized Riemann invariants | ASYMPTOTIC-EXPANSION | EQUATIONS | SOLVERS | PHYSICS, MATHEMATICAL | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EULERIAN GRP SCHEME | DYNAMICS | SYSTEMS | CONSERVATIVE DIFFERENCE SCHEME | Fluid dynamics | Glass fiber reinforced plastics | Discontinuity | Accuracy | Mathematical analysis | Evolution | Mathematical models | Rarefaction | Derivatives

GRP solver | Generalized Riemann problem | Generalized Riemann invariants | ASYMPTOTIC-EXPANSION | EQUATIONS | SOLVERS | PHYSICS, MATHEMATICAL | LAWS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EULERIAN GRP SCHEME | DYNAMICS | SYSTEMS | CONSERVATIVE DIFFERENCE SCHEME | Fluid dynamics | Glass fiber reinforced plastics | Discontinuity | Accuracy | Mathematical analysis | Evolution | Mathematical models | Rarefaction | Derivatives

Journal Article

Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 02/2002, Volume 458, Issue 2018, pp. 271 - 281

We present a method for solving the generalized Riemann problem for partial differential equations of the advection–reaction type. The generalization of the...

Conservation laws | Mathematical procedures | Error rates | Advection | Numerical methods | Scalars | Mathematical vectors | Riemann condition | Cauchy problem | Burger equation | Godunov | Advection-reaction | ADER | Generalized Riemann problem | advection-reaction | generalized Riemann problem | MULTIDISCIPLINARY SCIENCES

Conservation laws | Mathematical procedures | Error rates | Advection | Numerical methods | Scalars | Mathematical vectors | Riemann condition | Cauchy problem | Burger equation | Godunov | Advection-reaction | ADER | Generalized Riemann problem | advection-reaction | generalized Riemann problem | MULTIDISCIPLINARY SCIENCES

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 09/2012, Volume 64, Issue 6, pp. 1616 - 1626

We consider an initial value problem for a class of nonlinear fractional differential equations involving Hilfer fractional derivative. We prove existence and...

Fractional differential equation | Generalized Riemann–Liouville fractional derivative | Riemann–Liouville fractional derivative | Fractional derivatives | Caputo fractional derivative | Generalized Riemann-Liouville fractional derivative | Riemann-Liouville fractional derivative | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Fractional differential equation | Generalized Riemann–Liouville fractional derivative | Riemann–Liouville fractional derivative | Fractional derivatives | Caputo fractional derivative | Generalized Riemann-Liouville fractional derivative | Riemann-Liouville fractional derivative | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 386, Issue 1, pp. 343 - 363

A new concept of meromorphic Σ-factorization, for Hölder continuous functions defined on a contour Γ that is the pullback of R ˙ (or the unit circle) in a...

Riemann surfaces | Toeplitz operators | Factorization | Riemann–Hilbert problems | Riemann-Hilbert problems | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | GENERALIZED FACTORIZATION

Riemann surfaces | Toeplitz operators | Factorization | Riemann–Hilbert problems | Riemann-Hilbert problems | MATHEMATICS | MATHEMATICS, APPLIED | MATRIX FUNCTIONS | GENERALIZED FACTORIZATION

Journal Article