2015, ISBN 9781470417086, xxi, 253 p., 16 unnumbered p.s of plates

Lax, Peter D | Partial differential equations -- Hyperbolic equations and systems -- First-order hyperbolic systems | History and biography -- History of mathematics and mathematicians -- Biographies, obituaries, personalia, bibliographies | Partial differential equations -- Representations of solutions -- Soliton solutions | Partial differential equations -- General topics -- Propagation of singularities | Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Finite difference methods | Partial differential equations -- Equations of mathematical physics and other areas of application -- KdV-like equations (Korteweg-de Vries) | History and biography -- History of mathematics and mathematicians -- Schools of mathematics | Partial differential equations -- Hyperbolic equations and systems -- Wave equation | Fluid mechanics -- Shock waves and blast waves -- Shock waves and blast waves | Mathematicians

Book

Numerical Methods for Partial Differential Equations, ISSN 0749-159X, 05/2017, Volume 33, Issue 3, pp. 868 - 884

In this article, we extend the recently developed weak Galerkin method to solve the second‐order hyperbolic wave equation. Many nice features of the weak...

finite element method | second‐order hyperbolic equation | wave equation | weak Galerkin | second-order hyperbolic equation | MATHEMATICS, APPLIED | HELMHOLTZ-EQUATION | MESHES | 2ND-ORDER ELLIPTIC PROBLEMS | APPROXIMATIONS | BIHARMONIC EQUATION | HYPERBOLIC-EQUATIONS | FLOW | Finite element method | Analysis | Methods | Stability | Mathematical analysis | Wave equations | Exploration | Mathematical models | Galerkin methods | Convergence

finite element method | second‐order hyperbolic equation | wave equation | weak Galerkin | second-order hyperbolic equation | MATHEMATICS, APPLIED | HELMHOLTZ-EQUATION | MESHES | 2ND-ORDER ELLIPTIC PROBLEMS | APPROXIMATIONS | BIHARMONIC EQUATION | HYPERBOLIC-EQUATIONS | FLOW | Finite element method | Analysis | Methods | Stability | Mathematical analysis | Wave equations | Exploration | Mathematical models | Galerkin methods | Convergence

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2018, Volume 461, Issue 1, pp. 817 - 836

The article introduces a new general solution to a family of loaded ordinary differential equations and discusses its properties. It provides necessary and...

General solution | Solvability criteria | Algorithm | Loaded hyperbolic equations | MATHEMATICS | MATHEMATICS, APPLIED | 2 INDEPENDENT VARIABLES | DIFFERENTIAL-EQUATIONS

General solution | Solvability criteria | Algorithm | Loaded hyperbolic equations | MATHEMATICS | MATHEMATICS, APPLIED | 2 INDEPENDENT VARIABLES | DIFFERENTIAL-EQUATIONS

Journal Article

Advances in Water Resources, ISSN 0309-1708, 2011, Volume 34, Issue 9, pp. 1195 - 1206

► We describe the GeoClaw software for two-dimensional depth-averaged equations for geophysical flow problems. ► GeoClaw uses high-resolution shock-capturing...

Hyperbolic equations | Adaptive refinement | Numerical flow modeling | Finite volume methods | Depth-averaged equations | 3-DIMENSIONAL TERRAIN | WATER RESOURCES | MODEL | FINITE-VOLUME METHODS | SHALLOW-WATER EQUATIONS | AVALANCHES | WAVE-PROPAGATION ALGORITHMS | Software | Freeware | Wave propagation | Geophysics | Mathematical models | Source code | Computer programs | Drying

Hyperbolic equations | Adaptive refinement | Numerical flow modeling | Finite volume methods | Depth-averaged equations | 3-DIMENSIONAL TERRAIN | WATER RESOURCES | MODEL | FINITE-VOLUME METHODS | SHALLOW-WATER EQUATIONS | AVALANCHES | WAVE-PROPAGATION ALGORITHMS | Software | Freeware | Wave propagation | Geophysics | Mathematical models | Source code | Computer programs | Drying

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 2009, Volume 228, Issue 19, pp. 7426 - 7451

A novel high-resolution numerical method is presented for one-dimensional hyperbolic problems based on the extension of the original Upwind Leapfrog scheme to...

Hyperbolic equations | Advection schemes | Quasi-linear conservation laws | Computational fluid dynamics | FINITE-DIFFERENCE SCHEMES | EQUATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | LEAPFROG METHODS | PHYSICS, MATHEMATICAL | FLOW | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR PROBLEMS | UPWIND | SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | AEROACOUSTICS | Fluid dynamics | Environmental law | Analysis | Methods

Hyperbolic equations | Advection schemes | Quasi-linear conservation laws | Computational fluid dynamics | FINITE-DIFFERENCE SCHEMES | EQUATIONS | ESSENTIALLY NONOSCILLATORY SCHEMES | LEAPFROG METHODS | PHYSICS, MATHEMATICAL | FLOW | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NONLINEAR PROBLEMS | UPWIND | SYSTEMS | HYPERBOLIC CONSERVATION-LAWS | AEROACOUSTICS | Fluid dynamics | Environmental law | Analysis | Methods

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 03/2017, Volume 58, Issue 2, pp. 227 - 231

We state a new nonlocal boundary value problem for a mixed parabolic-hyperbolic equation. The equation is of the first kind, i.e., the curve on which the...

nonlocal boundary condition | Green’s function | parabolic-hyperbolic equation | Frankl problem | MATHEMATICS | BOUNDARY-VALUE-PROBLEM | Green's function | RECTANGULAR DOMAIN | TRICOMI

nonlocal boundary condition | Green’s function | parabolic-hyperbolic equation | Frankl problem | MATHEMATICS | BOUNDARY-VALUE-PROBLEM | Green's function | RECTANGULAR DOMAIN | TRICOMI

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2016, Volume 310, pp. 202 - 212

A flux-splitting method is proposed for the hyperbolic-equation system (HES) of magnetized electron fluids in quasi-neutral plasmas. The numerical fluxes are...

Plasma simulation | Upwind method | Electron fluid | Hyperbolic equation | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HALL THRUSTER | DIFFUSION | SIMULATIONS | MODEL | PHYSICS, MATHEMATICAL | HYBRID | Environmental law | Analysis | Methods | Fluids | Splitting | Computational fluid dynamics | Computation | Mathematical analysis | Fluid flow | Mathematical models | Plasmas | Physics - Computational Physics | FLUIDS | MAGNETIC FIELDS | PLASMA | PLASMA SIMULATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CONSERVATION LAWS | ADVECTION | EQUATIONS | STEADY-STATE CONDITIONS | ACCURACY

Plasma simulation | Upwind method | Electron fluid | Hyperbolic equation | SCHEME | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | HALL THRUSTER | DIFFUSION | SIMULATIONS | MODEL | PHYSICS, MATHEMATICAL | HYBRID | Environmental law | Analysis | Methods | Fluids | Splitting | Computational fluid dynamics | Computation | Mathematical analysis | Fluid flow | Mathematical models | Plasmas | Physics - Computational Physics | FLUIDS | MAGNETIC FIELDS | PLASMA | PLASMA SIMULATION | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | CONSERVATION LAWS | ADVECTION | EQUATIONS | STEADY-STATE CONDITIONS | ACCURACY

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 1, pp. 427 - 444

We establish a new Carleman inequality for linear Cahn–Hilliard type equation when the norms of right hand sides are in Sobolev spaces of negative orders, and...

Global Carleman estimate | Cahn–Hilliard type equation | Null controllability | Unique Continuation Property | MATHEMATICS | Cahn Hilliard type equation | HEAT-EQUATION | APPROXIMATE CONTROLLABILITY | HYPERBOLIC-EQUATIONS

Global Carleman estimate | Cahn–Hilliard type equation | Null controllability | Unique Continuation Property | MATHEMATICS | Cahn Hilliard type equation | HEAT-EQUATION | APPROXIMATE CONTROLLABILITY | HYPERBOLIC-EQUATIONS

Journal Article

Mathematical Notes, ISSN 0001-4346, 9/2017, Volume 102, Issue 3, pp. 424 - 428

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 2009, Volume 71, Issue 9, pp. 4115 - 4124

We consider the second order Cauchy problem where is a continuous function, and is a self-adjoint nonnegative operator with dense domain on a Hilbert space. It...

Degenerate hyperbolic equation | Continuity modulus | Gevrey spaces | Integro-differential hyperbolic equation | Uniqueness | Kirchhoff equations | MATHEMATICS | MATHEMATICS, APPLIED | SOLVABILITY

Degenerate hyperbolic equation | Continuity modulus | Gevrey spaces | Integro-differential hyperbolic equation | Uniqueness | Kirchhoff equations | MATHEMATICS | MATHEMATICS, APPLIED | SOLVABILITY

Journal Article

SIAM Journal on Applied Mathematics, ISSN 0036-1399, 2016, Volume 76, Issue 4, pp. 1658 - 1682

We analyze a one-dimensional (1D) model of molecules diffusing along a line of N cells that are connected via stochastically gated gap junctions. Each gate...

Piecewise determinist ic PDEs | Channel permeability | Diffusion | Gap junctions | gap junctions | APPROXIMATE TRAVELING-WAVES | MATHEMATICS, APPLIED | diffusion | VOLTAGE | channel permeability | CALCIUM WAVES | NOISE | MODEL | ION-CHANNEL STOCHASTICITY | ASTROCYTES | NEURONS | REACTION-HYPERBOLIC EQUATIONS | INOSITOL-TRISPHOSPHATE | piecewise deterministic PDEs

Piecewise determinist ic PDEs | Channel permeability | Diffusion | Gap junctions | gap junctions | APPROXIMATE TRAVELING-WAVES | MATHEMATICS, APPLIED | diffusion | VOLTAGE | channel permeability | CALCIUM WAVES | NOISE | MODEL | ION-CHANNEL STOCHASTICITY | ASTROCYTES | NEURONS | REACTION-HYPERBOLIC EQUATIONS | INOSITOL-TRISPHOSPHATE | piecewise deterministic PDEs

Journal Article

Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2018, Volume 19, Issue 9, pp. 1525 - 1530

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 05/2018, Volume 41, Issue 7, pp. 2639 - 2653

This paper deals with the energy decay estimates and infinite blow‐up phenomena for a strongly damped semilinear wave equation with logarithmic nonlinear...

infinite blow‐up | logarithmic nonlinear | source | energy decay estimates | strong damping | wave equation | infinite blow-up | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | HYPERBOLIC-EQUATIONS | Dirichlet problem | Estimates | Decay | Wave equations

infinite blow‐up | logarithmic nonlinear | source | energy decay estimates | strong damping | wave equation | infinite blow-up | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | HYPERBOLIC-EQUATIONS | Dirichlet problem | Estimates | Decay | Wave equations

Journal Article

Chaos, Solitons and Fractals, ISSN 0960-0779, 2009, Volume 41, Issue 3, pp. 1448 - 1453

In this work, the well known variational iteration method is used for solving the one-dimensional wave equation that combines classical and integral boundary...

NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | HYPERBOLIC EQUATION | APPROXIMATE SOLUTION | PARABOLIC EQUATION | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE | Methods | Universities and colleges

NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | HYPERBOLIC EQUATION | APPROXIMATE SOLUTION | PARABOLIC EQUATION | PHYSICS, MATHEMATICAL | FINITE-DIFFERENCE | Methods | Universities and colleges

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 230, Issue 2, pp. 626 - 632

In this paper, we propose a three level compact difference scheme of for the difference solution of a two-dimensional second-order non-homogeneous linear...

High accuracy | Compact difference scheme | Stability analysis | Linear hyperbolic equation | MATHEMATICS, APPLIED | ADI METHOD | VARIABLE-COEFFICIENTS

High accuracy | Compact difference scheme | Stability analysis | Linear hyperbolic equation | MATHEMATICS, APPLIED | ADI METHOD | VARIABLE-COEFFICIENTS

Journal Article

Journal of Evolution Equations, ISSN 1424-3199, 3/2018, Volume 18, Issue 1, pp. 105 - 125

In this paper, we consider a plate equation with a logarithmic nonlinearity in the presence of nonlinear frictional damping. Using the Galaerkin method, we...

Analysis | Mathematics | MATHEMATICS | DISSIPATION | MATHEMATICS, APPLIED | NONEXISTENCE | GLOBAL EXISTENCE | STABILIZATION | EXPONENTIAL DECAY | PETROVSKY | WAVE-EQUATION | HYPERBOLIC-EQUATIONS | BOUNDARY

Analysis | Mathematics | MATHEMATICS | DISSIPATION | MATHEMATICS, APPLIED | NONEXISTENCE | GLOBAL EXISTENCE | STABILIZATION | EXPONENTIAL DECAY | PETROVSKY | WAVE-EQUATION | HYPERBOLIC-EQUATIONS | BOUNDARY

Journal Article

DIFFERENTIAL AND INTEGRAL EQUATIONS, ISSN 0893-4983, 11/2016, Volume 29, Issue 11-12, pp. 1139 - 1166

In this paper, we discuss the Cauchy problem for a degenerate parabolic-hyperbolic equation with a multiplicative noise. We focus on the existence of a...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | SCALAR CONSERVATION-LAWS | HYPERBOLIC EQUATIONS | FORMULATION

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | SCALAR CONSERVATION-LAWS | HYPERBOLIC EQUATIONS | FORMULATION

Journal Article

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, ISSN 1991-8615, 03/2016, Volume 20, Issue 1, pp. 65 - 73

We consider three problems for hyperbolic equation on a plane in the characteristic domain. In these problems at least one of the conditions of the Goursat...

nonlocal conditions | the problem with displacement | hyperbolic equation

nonlocal conditions | the problem with displacement | hyperbolic equation

Journal Article

Materials Research, ISSN 1516-1439, 12/2015, Volume 18, Issue suppl 2, pp. 193 - 199

Fique is a plant native of Colombia with fibers extracted from its leaves presenting relevant physical characteristics and mechanical properties for possible...

Elastic modulus | Hyperbolic equation | Weibull analysis | Fique fiber | VEGETABLE FIBERS | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | COMPOSITES | weibull analysis | hyperbolic equation | MECHANICAL-PROPERTIES | GLASS | NATURAL FIBERS | BIOFIBRES | fique fiber | elastic modulus | REINFORCEMENT | BIOCOMPOSITES

Elastic modulus | Hyperbolic equation | Weibull analysis | Fique fiber | VEGETABLE FIBERS | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | COMPOSITES | weibull analysis | hyperbolic equation | MECHANICAL-PROPERTIES | GLASS | NATURAL FIBERS | BIOFIBRES | fique fiber | elastic modulus | REINFORCEMENT | BIOCOMPOSITES

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 01/2015, Volume 112, pp. 129 - 146

The initial–boundary value problem for some nonlinear higher-order viscoelastic wave equation with a nonlinear source term in a bounded domain is studied. The...

Nonlinear higher-order viscoelastic wave equation | Global existence | Lifespan estimate | Nonlinear source term | Blow-up | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | NONEXISTENCE | DECAY | HYPERBOLIC-EQUATIONS | Viscoelasticity | Boundary value problems | Mathematical analysis | Wave equations | Nonlinearity | Initial value problems | Energy of solution | Galerkin methods

Nonlinear higher-order viscoelastic wave equation | Global existence | Lifespan estimate | Nonlinear source term | Blow-up | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY | NONEXISTENCE | DECAY | HYPERBOLIC-EQUATIONS | Viscoelasticity | Boundary value problems | Mathematical analysis | Wave equations | Nonlinearity | Initial value problems | Energy of solution | Galerkin methods

Journal Article

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