Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 1 - 19

The aim of this paper is to consider a class of degenerate damped hyperbolic equations with the critical nonlinearity involving an operator L that is...

Semilinear degenerate damped hyperbolic equation | Critical growth | Global attractor | MATHEMATICS | MATHEMATICS, APPLIED | X-ELLIPTIC OPERATORS | THEOREM | HARNACK INEQUALITY | hyperbolic equation | Semilinear degenerate damped

Semilinear degenerate damped hyperbolic equation | Critical growth | Global attractor | MATHEMATICS | MATHEMATICS, APPLIED | X-ELLIPTIC OPERATORS | THEOREM | HARNACK INEQUALITY | hyperbolic equation | Semilinear degenerate damped

Journal Article

Communications in Mathematical Sciences, ISSN 1539-6746, 2017, Volume 15, Issue 7, pp. 2055 - 2085

Metastable dynamics of a hyperbolic variation of the Allen-Cahn equation with homogeneous Neumann boundary conditions are considered. Using the "dynamical...

Singular perturbations | Allen-Cahn equation | Metastability | singular perturbations | MATHEMATICS, APPLIED | BOUNDARY MOTION | metastability | BISTABLE NONLINEARITY | PATTERNS | SINGULAR LIMIT | SLOW MOTION | ONE SPACE DIMENSION | HILLIARD EQUATION | BURGERS-EQUATION | DAMPED WAVE-EQUATION | HEAT WAVES | Mathematics - Analysis of PDEs

Singular perturbations | Allen-Cahn equation | Metastability | singular perturbations | MATHEMATICS, APPLIED | BOUNDARY MOTION | metastability | BISTABLE NONLINEARITY | PATTERNS | SINGULAR LIMIT | SLOW MOTION | ONE SPACE DIMENSION | HILLIARD EQUATION | BURGERS-EQUATION | DAMPED WAVE-EQUATION | HEAT WAVES | Mathematics - Analysis of PDEs

Journal Article

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Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations

Journal of Differential Equations, ISSN 0022-0396, 02/2018, Volume 264, Issue 3, pp. 1886 - 1945

In this work we prove the lower and upper semicontinuity of pullback, uniform, and cocycle attractors for the non-autonomous dynamical system given by...

Continuity of attractors | Damped wave equation | Non-autonomous dynamical systems | Uniform attractor | Hyperbolic perturbation | MATHEMATICS | DYNAMICS | DIFFERENTIAL-EQUATIONS | EXPONENTIAL ATTRACTORS | ASYMPTOTIC REGULARITY | DAMPED WAVE-EQUATIONS

Continuity of attractors | Damped wave equation | Non-autonomous dynamical systems | Uniform attractor | Hyperbolic perturbation | MATHEMATICS | DYNAMICS | DIFFERENTIAL-EQUATIONS | EXPONENTIAL ATTRACTORS | ASYMPTOTIC REGULARITY | DAMPED WAVE-EQUATIONS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2017, Volume 73, Issue 4, pp. 560 - 564

This paper is concerned with the blow-up of solutions to a superlinear hyperbolic equation with linear damping term utt−Δu−ωΔut+μut=|u|p−2u,in[0,T]×Ω, where...

Damping term | Lower bounds for the blow-up time | Hyperbolic equation | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CHEMOTAXIS SYSTEM | DAMPED WAVE-EQUATION

Damping term | Lower bounds for the blow-up time | Hyperbolic equation | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | CHEMOTAXIS SYSTEM | DAMPED WAVE-EQUATION

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 10/2016, Volume 60, pp. 115 - 119

This paper deals with the lower bound for blow-up solutions to a nonlinear viscoelastic hyperbolic equation. An inverse Hölder inequality with the correction...

Viscoelastic hyperbolic equation | Lower bound estimate | Energy estimate method | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | DAMPED WAVE-EQUATION | Viscoelasticity | Lower bounds | Mathematical analysis | Inequalities | Nonlinearity | Constants | Inverse | Sun

Viscoelastic hyperbolic equation | Lower bound estimate | Energy estimate method | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | DAMPED WAVE-EQUATION | Viscoelasticity | Lower bounds | Mathematical analysis | Inequalities | Nonlinearity | Constants | Inverse | Sun

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 04/2017, Volume 334, pp. 392 - 418

In the numerical solution of Maxwell's equations for dynamic electromagnetic fields, the two Gauss's laws are usually not considered since they are a natural...

Discontinuous Galerkin time-domain method | Self-consistent simulation | Divergence-cleaning | Electromagnetic simulation | Damped hyperbolic Maxwell equations | Inhomogeneous media | Continuity-preserving | Purely hyperbolic Maxwell equations | TIME-DOMAIN | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VECTOR BASIS FUNCTIONS | Algorithms | Electromagnetism | Electromagnetic fields | Environmental law

Discontinuous Galerkin time-domain method | Self-consistent simulation | Divergence-cleaning | Electromagnetic simulation | Damped hyperbolic Maxwell equations | Inhomogeneous media | Continuity-preserving | Purely hyperbolic Maxwell equations | TIME-DOMAIN | DISCONTINUOUS GALERKIN METHOD | PHYSICS, MATHEMATICAL | ORDER | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | VECTOR BASIS FUNCTIONS | Algorithms | Electromagnetism | Electromagnetic fields | Environmental law

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2007, Volume 187, Issue 2, pp. 1272 - 1276

A few explicit difference schemes are discussed for the numerical solution of the linear hyperbolic equation u tt + 2 α u t + β 2 u = u xx + f( x, t), α > 0, β...

Second-order linear hyperbolic equation | Damped wave equation | Unconditionally stable | Explicit scheme | Pade approximation | Telegraph equation | MATHEMATICS, APPLIED | telegraph equation | explicit scheme | pade approximation | damped wave equation | second-order linear hyperbolic equation | unconditionally stable

Second-order linear hyperbolic equation | Damped wave equation | Unconditionally stable | Explicit scheme | Pade approximation | Telegraph equation | MATHEMATICS, APPLIED | telegraph equation | explicit scheme | pade approximation | damped wave equation | second-order linear hyperbolic equation | unconditionally stable

Journal Article

International Journal of Computational Methods, ISSN 0219-8762, 02/2019, Volume 16, Issue 1

In this paper, we study a new numerical method of order 4 in space and time based on half-step discretization for the solution of three-space dimensional...

Van der Pol equation | wave equation with singular coefficients | operator splitting method | half-step discretization | Three-space dimensional quasilinear hyperbolic equation | damped wave equation | APPROXIMATION | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | VARIABLE-COEFFICIENTS | ENGINEERING, MULTIDISCIPLINARY | HIGHER-ORDER | ADER SCHEMES

Van der Pol equation | wave equation with singular coefficients | operator splitting method | half-step discretization | Three-space dimensional quasilinear hyperbolic equation | damped wave equation | APPROXIMATION | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | VARIABLE-COEFFICIENTS | ENGINEERING, MULTIDISCIPLINARY | HIGHER-ORDER | ADER SCHEMES

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 05/2019, Volume 182, pp. 57 - 74

This paper is concerned with the blowup phenomena for initial–boundary value problem...

Evolution equations | Critical case | Upper bound of lifespan | Small data blow-up | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | DAMPED WAVE-EQUATIONS | CAUCHY-PROBLEM | NONLINEAR SCHRODINGER-EQUATION | DATA BLOW-UP | MATHEMATICS | CRITICAL EXPONENT | GINZBURG-LANDAU EQUATION | DIFFUSION | Boundary value problems | Parameters | Life span | Upper bounds | Test procedures | Smooth boundaries | Queuing theory

Evolution equations | Critical case | Upper bound of lifespan | Small data blow-up | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | DAMPED WAVE-EQUATIONS | CAUCHY-PROBLEM | NONLINEAR SCHRODINGER-EQUATION | DATA BLOW-UP | MATHEMATICS | CRITICAL EXPONENT | GINZBURG-LANDAU EQUATION | DIFFUSION | Boundary value problems | Parameters | Life span | Upper bounds | Test procedures | Smooth boundaries | Queuing theory

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2014, Volume 244, pp. 624 - 641

In this article, we describe a new compact three level implicit method of order four in time and space based on half-step discretization for one space...

Damped wave equation | Van der Pol type nonlinear wave equation | Stability | Singular coefficients | Half-step discretization | Quasilinear hyperbolic equation | MATHEMATICS, APPLIED | WAVE-EQUATION | SCHEMES | Algorithms

Damped wave equation | Van der Pol type nonlinear wave equation | Stability | Singular coefficients | Half-step discretization | Quasilinear hyperbolic equation | MATHEMATICS, APPLIED | WAVE-EQUATION | SCHEMES | Algorithms

Journal Article

International Journal of Control, ISSN 0020-7179, 11/2019, Volume 92, Issue 11, pp. 2484 - 2498

The present work proposes an extension of single-step formulation of full-state feedback control design to the class of distributed parameter system described...

single-step full-state feedback design | distributed-parameter systems | Lyapunov's auxiliary theorem | exothermic plug-flow reactor | damped wave equation | LINEARIZATION | SINGULAR PDES | INFINITE DIMENSIONAL SYSTEMS | BOUNDARY | FORMULATION | AUTOMATION & CONTROL SYSTEMS | State feedback | Coordinate transformations | Nonlinear equations | Partial differential equations | Mathematical analysis | Exothermic reactions | Control systems | Plug flow chemical reactors | Control theory | Feedback control | Nonlinear control

single-step full-state feedback design | distributed-parameter systems | Lyapunov's auxiliary theorem | exothermic plug-flow reactor | damped wave equation | LINEARIZATION | SINGULAR PDES | INFINITE DIMENSIONAL SYSTEMS | BOUNDARY | FORMULATION | AUTOMATION & CONTROL SYSTEMS | State feedback | Coordinate transformations | Nonlinear equations | Partial differential equations | Mathematical analysis | Exothermic reactions | Control systems | Plug flow chemical reactors | Control theory | Feedback control | Nonlinear control

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 10, pp. 5133 - 5159

We consider the large time behavior of the radially symmetric solution to the equation for a quasilinear hyperbolic model in the exterior domain of a ball in...

Damped wave equation | Galerkin method | Stationary wave | Asymptotic behavior | SPACE | MATHEMATICS | NONCONVEX CONVECTION | NAVIER-STOKES EQUATIONS | GLOBAL EXISTENCE | DAMPED WAVE-EQUATIONS | BURGERS-EQUATION

Damped wave equation | Galerkin method | Stationary wave | Asymptotic behavior | SPACE | MATHEMATICS | NONCONVEX CONVECTION | NAVIER-STOKES EQUATIONS | GLOBAL EXISTENCE | DAMPED WAVE-EQUATIONS | BURGERS-EQUATION

Journal Article

Siberian Mathematical Journal, ISSN 0037-4466, 7/2016, Volume 57, Issue 4, pp. 632 - 649

We investigate the asymptotic behavior of solutions to damped hyperbolic equations involving strongly degenerate differential operators. First we establish the...

Lyapunov functional | global attractor | degenerate damped hyperbolic equation | l-trajectory | finite dimensionality of attractors | Mathematics, general | Mathematics | global solution | MATHEMATICS | ATTRACTORS | OPERATORS

Lyapunov functional | global attractor | degenerate damped hyperbolic equation | l-trajectory | finite dimensionality of attractors | Mathematics, general | Mathematics | global solution | MATHEMATICS | ATTRACTORS | OPERATORS

Journal Article

Numerische Mathematik, ISSN 0029-599X, 7/2013, Volume 124, Issue 3, pp. 559 - 601

This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic...

Mathematical Methods in Physics | 65P99 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | 35B10 | Mathematics, general | Mathematics | 93C20 | SPACE SEMI-DISCRETIZATIONS | BOUNDARY OBSERVABILITY | MATHEMATICS, APPLIED | EXPONENTIALLY STABLE APPROXIMATIONS | HELMHOLTZ-EQUATION | STABILIZATION | DAMPED WAVE-EQUATION | Algorithms | Resveratrol

Mathematical Methods in Physics | 65P99 | Numerical Analysis | Theoretical, Mathematical and Computational Physics | Appl.Mathematics/Computational Methods of Engineering | Numerical and Computational Physics | 35B10 | Mathematics, general | Mathematics | 93C20 | SPACE SEMI-DISCRETIZATIONS | BOUNDARY OBSERVABILITY | MATHEMATICS, APPLIED | EXPONENTIALLY STABLE APPROXIMATIONS | HELMHOLTZ-EQUATION | STABILIZATION | DAMPED WAVE-EQUATION | Algorithms | Resveratrol

Journal Article

Nonlinearity, ISSN 0951-7715, 02/2016, Volume 29, Issue 4, pp. 1171 - 1212

We establish the well-posedness of a strongly damped semilinear wave equation equipped with nonlinear hyperbolic dynamic boundary conditions. Results are...

35L71; Secondary: 35Q74 | global attractor | weak exponential attractor Mathematics Subject Classification numbers: Primary: 35B41 | damped wave equation | hyperbolic dynamic boundary condition | semilinear hyperbolic equation | 35L20 | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | ELASTIC-SYSTEMS | CAHN-HILLIARD EQUATION | R-3 | weak exponential attractor | PHYSICS, MATHEMATICAL | Nonlinear dynamics | Perturbation methods | Mathematical analysis | Fractal analysis | Wave equations | Nonlinearity | Boundary conditions | Topology | Mathematics - Analysis of PDEs

35L71; Secondary: 35Q74 | global attractor | weak exponential attractor Mathematics Subject Classification numbers: Primary: 35B41 | damped wave equation | hyperbolic dynamic boundary condition | semilinear hyperbolic equation | 35L20 | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | ELASTIC-SYSTEMS | CAHN-HILLIARD EQUATION | R-3 | weak exponential attractor | PHYSICS, MATHEMATICAL | Nonlinear dynamics | Perturbation methods | Mathematical analysis | Fractal analysis | Wave equations | Nonlinearity | Boundary conditions | Topology | Mathematics - Analysis of PDEs

Journal Article

Quarterly of Applied Mathematics, ISSN 0033-569X, 2015, Volume 73, Issue 1, pp. 93 - 129

Under consideration is the hyperbolic relaxation of a semilinear reaction-diffusion equation epsilon u(u) + u(l) - Delta u + f(u) - 0 on a bounded domain Omega...

Upper semicontinuity | Singular perturbation | Damped wave equation | Dynamic boundary condition | Hyperbolic relaxation | Semilinear reaction diffusion equation | Global attractor | semilinear reaction diffusion equation | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | global attractor | singular perturbation | PARABOLIC EQUATIONS | SEMILINEAR WAVE-EQUATION | hyperbolic relaxation | NONLINEAR BOUNDARY | MEMORY | upper-semicontinuity | INTERIOR | damped wave equation | CAHN-HILLIARD EQUATIONS | WEAK SOLUTIONS

Upper semicontinuity | Singular perturbation | Damped wave equation | Dynamic boundary condition | Hyperbolic relaxation | Semilinear reaction diffusion equation | Global attractor | semilinear reaction diffusion equation | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | global attractor | singular perturbation | PARABOLIC EQUATIONS | SEMILINEAR WAVE-EQUATION | hyperbolic relaxation | NONLINEAR BOUNDARY | MEMORY | upper-semicontinuity | INTERIOR | damped wave equation | CAHN-HILLIARD EQUATIONS | WEAK SOLUTIONS

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 03/2007, Volume 17, Issue 3, pp. 411 - 437

In this paper we consider the hyperbolic relaxation of the Cahn-Hilliard equation ruling the evolution of the relative concentration u of one component of a...

Cahn-Hilliard equation | Approximation of global attractors | Hyperbolic relaxation | Damped semilinear wave equation | Generalized semiflows | Global attractor | SYSTEM | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | ENERGY | global attractor | GLOBAL ATTRACTORS | SPINODAL DECOMPOSITION | MODEL | hyperbolic relaxation | generalized semiflows | CONTINUITY | damped semilinear wave equation | HIGHER DIMENSIONS | approximation of global attractors | WAVE-EQUATIONS | UPPER SEMICONTINUITY

Cahn-Hilliard equation | Approximation of global attractors | Hyperbolic relaxation | Damped semilinear wave equation | Generalized semiflows | Global attractor | SYSTEM | MATHEMATICS, APPLIED | EXPONENTIAL ATTRACTORS | ENERGY | global attractor | GLOBAL ATTRACTORS | SPINODAL DECOMPOSITION | MODEL | hyperbolic relaxation | generalized semiflows | CONTINUITY | damped semilinear wave equation | HIGHER DIMENSIONS | approximation of global attractors | WAVE-EQUATIONS | UPPER SEMICONTINUITY

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 04/2017, Volume 38, Issue 4, pp. 466 - 485

In this article, we derive error estimates for the semi-discrete and fully discrete Galerkin approximations of a general linear second-order hyperbolic partial...

65M15 | Galerkin approximation | 65M60 | second-order hyperbolic equation | Damped vibration | error estimates | finite elements | BEAM | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | WAVE-EQUATION | Finite element method | Damping | Partial differential equations | Differential equations | Galerkin method | Boundary damping | Estimates | Elastic bodies | Errors | Approximation | Mathematical analysis | Complement | Galerkin methods

65M15 | Galerkin approximation | 65M60 | second-order hyperbolic equation | Damped vibration | error estimates | finite elements | BEAM | MATHEMATICS, APPLIED | BOUNDARY-CONDITIONS | WAVE-EQUATION | Finite element method | Damping | Partial differential equations | Differential equations | Galerkin method | Boundary damping | Estimates | Elastic bodies | Errors | Approximation | Mathematical analysis | Complement | Galerkin methods

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 2008, Volume 245, Issue 10, pp. 2979 - 3007

We consider the second order Cauchy problem ε u ε ″ + u ε ′ + m ( | A 1 / 2 u ε | 2 ) A u ε = 0 , u ε ( 0 ) = u 0 , u ε ′ ( 0 ) = u 1 , and the first order...

Singular perturbations | Degenerate damped hyperbolic equations | Degenerate parabolic equations | Kirchhoff equations | Decay rate of solutions | MATHEMATICS | GLOBAL EXISTENCE | STABILITY | SOLVABILITY | NONLINEAR-WAVE EQUATIONS | ASYMPTOTIC-BEHAVIOR | UNIQUENESS

Singular perturbations | Degenerate damped hyperbolic equations | Degenerate parabolic equations | Kirchhoff equations | Decay rate of solutions | MATHEMATICS | GLOBAL EXISTENCE | STABILITY | SOLVABILITY | NONLINEAR-WAVE EQUATIONS | ASYMPTOTIC-BEHAVIOR | UNIQUENESS

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/2014, Volume 55, Issue 12, p. 121504

In this paper, we are concerned with the asymptotic behaviour of weak solutions to the initial boundary value problem for a class of quasilinear hyperbolic...

EXISTENCE | DISSIPATION | ENERGY | THEOREMS | VISCOELASTIC EQUATION | EVOLUTION-EQUATIONS | UNIFORM DECAY | PHYSICS, MATHEMATICAL | DAMPED WAVE-EQUATION | ASYMPTOTIC-BEHAVIOR | Damping | Boundary value problems | Decay rate | Asymptotic properties | Mathematical analysis | Decay

EXISTENCE | DISSIPATION | ENERGY | THEOREMS | VISCOELASTIC EQUATION | EVOLUTION-EQUATIONS | UNIFORM DECAY | PHYSICS, MATHEMATICAL | DAMPED WAVE-EQUATION | ASYMPTOTIC-BEHAVIOR | Damping | Boundary value problems | Decay rate | Asymptotic properties | Mathematical analysis | Decay

Journal Article

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