Nonlinear Analysis, ISSN 0362-546X, 12/2019, Volume 189, p. 111582

Under consideration is the damped semilinear wave equation utt+ut−Δu+u+f(u)=0on a bounded domain Ω in R3 with a perturbation parameter ε>0 occurring in an...

Robin boundary condition | Singular perturbation | Upper-semicontinuity | Exponential attractor | Damped semilinear wave equation | Acoustic boundary condition | Global attractor | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, APPLIED | GLOBAL ATTRACTORS | HYPERBOLIC RELAXATION | MATHEMATICS | MEMORY | ROBUST EXPONENTIAL ATTRACTORS | CAHN-HILLIARD EQUATIONS | Boundary conditions | Parameters | Perturbation | Asymptotic methods | Wave equations

Robin boundary condition | Singular perturbation | Upper-semicontinuity | Exponential attractor | Damped semilinear wave equation | Acoustic boundary condition | Global attractor | REACTION-DIFFUSION EQUATIONS | MATHEMATICS, APPLIED | GLOBAL ATTRACTORS | HYPERBOLIC RELAXATION | MATHEMATICS | MEMORY | ROBUST EXPONENTIAL ATTRACTORS | CAHN-HILLIARD EQUATIONS | Boundary conditions | Parameters | Perturbation | Asymptotic methods | Wave equations

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 6944 - 6975

We investigate the asymptotic periodicity, Lp‐boundedness, classical (resp., strong) solutions, and the topological structure of solutions set of strongly...

strong solutions | asymptotic behavior | classical solutions | boundedness | topological structure of solutions set | damped wave equations | Strong solutionstopological structure of solutions set | Damped wave equations | Asymptotic behavior | Boundedness | Classical solutions | EXISTENCE | MATHEMATICS, APPLIED | PERIODIC-FUNCTIONS | BEHAVIOR | CRITICAL NONLINEARITIES | DIFFERENTIAL-EQUATIONS | ATTRACTORS | REGULARITY | SYSTEMS | BLOW-UP | DOMAINS | Periodic variations | Mathematical analysis | Wave equations

strong solutions | asymptotic behavior | classical solutions | boundedness | topological structure of solutions set | damped wave equations | Strong solutionstopological structure of solutions set | Damped wave equations | Asymptotic behavior | Boundedness | Classical solutions | EXISTENCE | MATHEMATICS, APPLIED | PERIODIC-FUNCTIONS | BEHAVIOR | CRITICAL NONLINEARITIES | DIFFERENTIAL-EQUATIONS | ATTRACTORS | REGULARITY | SYSTEMS | BLOW-UP | DOMAINS | Periodic variations | Mathematical analysis | Wave equations

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 06/2018, Volume 41, Issue 9, pp. 3476 - 3494

The main purpose of the current paper is to propose a new numerical scheme based on the spectral element procedure for simulating the neutral delay...

finite difference scheme and energy method | fractional damped diffusion‐wave equation | spectral element method | distributed‐order fractional equation | fractional delay PDE | stability and convergence analysis | distributed-order fractional equation | fractional damped diffusion-wave equation | MATHEMATICS, APPLIED | 2ND-ORDER | STABILITY | TIME-DELAY | POLYNOMIALS | PREDATOR-PREY SYSTEM | SCHEME | NUMERICAL-SOLUTION | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICS | COLLOCATION | Finite element method | Computer simulation | Wave equations | Spectral element method | Spectra | Delay | Convergence

finite difference scheme and energy method | fractional damped diffusion‐wave equation | spectral element method | distributed‐order fractional equation | fractional delay PDE | stability and convergence analysis | distributed-order fractional equation | fractional damped diffusion-wave equation | MATHEMATICS, APPLIED | 2ND-ORDER | STABILITY | TIME-DELAY | POLYNOMIALS | PREDATOR-PREY SYSTEM | SCHEME | NUMERICAL-SOLUTION | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICS | COLLOCATION | Finite element method | Computer simulation | Wave equations | Spectral element method | Spectra | Delay | Convergence

Journal Article

Discrete and Continuous Dynamical Systems, ISSN 1078-0947, 01/2004, Volume 10, Issue 1-2, pp. 31 - 52

The existence of a global attractor in the natural energy space is proved for the semilinear wave equation u(tt) + betau(t) - Deltau + f(u) = 0 on a bounded...

Nonuniqueness | Weakly continuous | Semilinear wave equation | Weak solution | Asymptotically smooth | Kneser's property | Damped | Asymptotically compact | Generalized semi-flow | Global attractor | Lyapunov function | MATHEMATICS, APPLIED | generalized semiflow | global attractor | nonuniqueness | GORDON-SCHRODINGER EQUATION | EVOLUTION-EQUATIONS | weakly continuous | ASYMPTOTIC-BEHAVIOR | semilinear wave equation | MATHEMATICS | damped | weak solution | PARTIAL-DIFFERENTIAL EQUATION | CRITICAL EXPONENT | ANALYTIC NONLINEARITY | asymptotically compact | SUPERCRITICAL EXPONENT | CONVERGENCE | UNBOUNDED-DOMAINS | WEAK SOLUTIONS | asymptotically smooth

Nonuniqueness | Weakly continuous | Semilinear wave equation | Weak solution | Asymptotically smooth | Kneser's property | Damped | Asymptotically compact | Generalized semi-flow | Global attractor | Lyapunov function | MATHEMATICS, APPLIED | generalized semiflow | global attractor | nonuniqueness | GORDON-SCHRODINGER EQUATION | EVOLUTION-EQUATIONS | weakly continuous | ASYMPTOTIC-BEHAVIOR | semilinear wave equation | MATHEMATICS | damped | weak solution | PARTIAL-DIFFERENTIAL EQUATION | CRITICAL EXPONENT | ANALYTIC NONLINEARITY | asymptotically compact | SUPERCRITICAL EXPONENT | CONVERGENCE | UNBOUNDED-DOMAINS | WEAK SOLUTIONS | asymptotically smooth

Journal Article

数学年刊：B辑英文版, ISSN 0252-9599, 2013, Volume 34, Issue 3, pp. 345 - 380

The authors study the Cauchy problem for the semi-linear damped wave equation utt-△u＋b（t）ut=f（u）,u（0,χ）=u0（χ）,ut（0,χ）=u1（χ） in any space dimension n ≥ 1. It is...

整体存在性 | 空间维度 | 时间相关 | 阻尼波动方程 | 阻尼项 | UT斯达康 | 半线性波动方程 | Cauchy问题 | 35L71 | Mathematics, general | Semi-linear equations | Global existence | Mathematics | Critical exponent | Applications of Mathematics | Damped wave equations | EXISTENCE | MATHEMATICS | R-N | CAUCHY-PROBLEM | Computer science | Analysis | Universities and colleges | Mathematics - Analysis of PDEs

整体存在性 | 空间维度 | 时间相关 | 阻尼波动方程 | 阻尼项 | UT斯达康 | 半线性波动方程 | Cauchy问题 | 35L71 | Mathematics, general | Semi-linear equations | Global existence | Mathematics | Critical exponent | Applications of Mathematics | Damped wave equations | EXISTENCE | MATHEMATICS | R-N | CAUCHY-PROBLEM | Computer science | Analysis | Universities and colleges | Mathematics - Analysis of PDEs

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 04/2013, Volume 254, Issue 8, pp. 3352 - 3368

We study the Cauchy problem for abstract dissipative equations in Hilbert spaces generalizing wave equations with strong damping terms in RN or exterior...

Strongly damped wave equation | Multiplier method | Fourier analysis | Total energy decay | High frequency | Low frequency | Spectral analysis | EXISTENCE | DISSIPATION | DECAY | EVOLUTION-EQUATIONS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | EXTERIOR DOMAINS | DIFFUSION PHENOMENON | SYSTEMS

Strongly damped wave equation | Multiplier method | Fourier analysis | Total energy decay | High frequency | Low frequency | Spectral analysis | EXISTENCE | DISSIPATION | DECAY | EVOLUTION-EQUATIONS | ASYMPTOTIC-BEHAVIOR | MATHEMATICS | EXTERIOR DOMAINS | DIFFUSION PHENOMENON | SYSTEMS

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2019, Volume 22, Issue 4, pp. 990 - 1013

In this paper, for the high frequency part of the solution , ) to the linear fractional damped wave equation, we derive asymptotic-in-time linear estimates in...

Primary 35L05 | 42B35 42B37 | damped fractional wave equation | Secondary 42B30 | Triebel-Lizorkin space | Hardy space | MATHEMATICS | MATHEMATICS, APPLIED | R-N | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | BOUNDEDNESS | DIFFUSION | L-P | Estimates | Wave equations

Primary 35L05 | 42B35 42B37 | damped fractional wave equation | Secondary 42B30 | Triebel-Lizorkin space | Hardy space | MATHEMATICS | MATHEMATICS, APPLIED | R-N | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SPACES | BOUNDEDNESS | DIFFUSION | L-P | Estimates | Wave equations

Journal Article

IEEE Transactions on Intelligent Transportation Systems, ISSN 1524-9050, 09/2018, Volume 19, Issue 9, pp. 2955 - 2964

Traffic congestion wastes fuel and commuters' time, and adds to CO 2 emissions. Stop-and-go traffic instabilities can be suppresses using bilateral...

Propagation | car following model | phantom traffic jam elimination | Control systems | Stability analysis | Automobiles | adaptive cruise control | advanced cruise control | Traffic flow instabilities | Perturbation methods | damped wave equation | stop-and-go traffic prevention | Acceleration | Mathematical model | bilateral control | CAR-FOLLOWING MODEL | STATES | PHASE-TRANSITIONS | STABILITY | SPEED LIMITS | ENGINEERING, ELECTRICAL & ELECTRONIC | HIGHWAY | CRUISE CONTROL | ENGINEERING, CIVIL | DYNAMICS | TRANSPORTATION SCIENCE & TECHNOLOGY | SYSTEMS | PHYSICS | Car following | Decay rate | Dampers | Computer simulation | Wave equations | Adaptive control | Cruise control | Vehicles | Traffic flow | Traffic speed | Traffic control | Springs (elastic) | Traffic congestion

Propagation | car following model | phantom traffic jam elimination | Control systems | Stability analysis | Automobiles | adaptive cruise control | advanced cruise control | Traffic flow instabilities | Perturbation methods | damped wave equation | stop-and-go traffic prevention | Acceleration | Mathematical model | bilateral control | CAR-FOLLOWING MODEL | STATES | PHASE-TRANSITIONS | STABILITY | SPEED LIMITS | ENGINEERING, ELECTRICAL & ELECTRONIC | HIGHWAY | CRUISE CONTROL | ENGINEERING, CIVIL | DYNAMICS | TRANSPORTATION SCIENCE & TECHNOLOGY | SYSTEMS | PHYSICS | Car following | Decay rate | Dampers | Computer simulation | Wave equations | Adaptive control | Cruise control | Vehicles | Traffic flow | Traffic speed | Traffic control | Springs (elastic) | Traffic congestion

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 06/2018, Volume 264, Issue 12, pp. 7023 - 7054

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the...

Damped wave equation | Unbounded damping | Quadratic operator function with unbounded coefficients | Schrödinger operators with complex potentials | Essential spectrum

Damped wave equation | Unbounded damping | Quadratic operator function with unbounded coefficients | Schrödinger operators with complex potentials | Essential spectrum

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2017, Volume 263, Issue 9, pp. 5377 - 5394

The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent,...

Damped wave equation | Semilinear | Blow-up | MATHEMATICS | TIME-DEPENDENT DISSIPATION | LIFE-SPAN | Information science | Mathematics - Analysis of PDEs

Damped wave equation | Semilinear | Blow-up | MATHEMATICS | TIME-DEPENDENT DISSIPATION | LIFE-SPAN | Information science | Mathematics - Analysis of PDEs

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 03/2018, Volume 168, pp. 222 - 237

It is well-known that the critical exponent for semilinear damped wave equations is Fujita exponent when the damping is effective. Lai, Takamura and Wakasa in...

Damped wave equation | Lifespan | Semilinear | Blow-up | MATHEMATICS | LIFE-SPAN | MATHEMATICS, APPLIED | DIMENSION | TIME-DEPENDENT DISSIPATION

Damped wave equation | Lifespan | Semilinear | Blow-up | MATHEMATICS | LIFE-SPAN | MATHEMATICS, APPLIED | DIMENSION | TIME-DEPENDENT DISSIPATION

Journal Article

12.
Full Text
A shift in the Strauss exponent for semilinear wave equations with a not effective damping

Journal of Differential Equations, ISSN 0022-0396, 11/2015, Volume 259, Issue 10, pp. 5040 - 5073

In this note we study the global existence of small data solutions to the Cauchy problem for the semilinear wave equation with a not effective scale-invariant...

Small data global existence | Strauss exponent | Not effective damping | Semilinear damped wave equation | MATHEMATICS | LIFE-SPAN | 3 SPACE DIMENSIONS | GLOBAL EXISTENCE | TIME BLOW-UP

Small data global existence | Strauss exponent | Not effective damping | Semilinear damped wave equation | MATHEMATICS | LIFE-SPAN | 3 SPACE DIMENSIONS | GLOBAL EXISTENCE | TIME BLOW-UP

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 10/2018, Volume 25, Issue 5, pp. 1 - 19

In this paper, we consider the Cauchy problem in $$\mathbb {R}^n,$$ Rn, $$n\ge 1,$$ n≥1, for semilinear damped wave equations with space–time dependent...

Local existence | Nonlinear damped wave equation | 35L70 | Analysis | 34B44 | 35B33 | 35L15 | Mathematics | Subcritical potential | Blow-up | MATHEMATICS, APPLIED | CRITICAL EXPONENT | GLOBAL EXISTENCE | STABILITY | EVOLUTION-EQUATIONS

Local existence | Nonlinear damped wave equation | 35L70 | Analysis | 34B44 | 35B33 | 35L15 | Mathematics | Subcritical potential | Blow-up | MATHEMATICS, APPLIED | CRITICAL EXPONENT | GLOBAL EXISTENCE | STABILITY | EVOLUTION-EQUATIONS

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2017, Volume 40, Issue 1, pp. 319 - 324

We study the exact controllability of q uncoupled damped string equations by means of the same control function. This property is called simultaneous...

exact controllability | simultaneous controllability | damped wave | MATHEMATICS, APPLIED | OBSERVABILITY | Functions (mathematics) | Damping | Stability | Mathematical analysis | Wave equations | Inequalities | Controllability | Strings

exact controllability | simultaneous controllability | damped wave | MATHEMATICS, APPLIED | OBSERVABILITY | Functions (mathematics) | Damping | Stability | Mathematical analysis | Wave equations | Inequalities | Controllability | Strings

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 04/2015, Volume 38, Issue 6, pp. 1032 - 1045

In this paper, we obtain the global existence of small data solutions to the Cauchy problem utt−Δu+μ1+tut=|u|pu(0,x)=u0(x),ut(0,x)=u1(x) in space dimension n ≥...

semilinear equations | global existence | damped waves | critical exponent | propagation speed | scale‐invariant | effective damping | scale-invariant | MATHEMATICS, APPLIED | R-N | BLOW-UP | Eulers equations | Damping | Decay rate | Thresholds | Sobolev space | Mathematical analysis | Estimates | Energy of solution | Cauchy problem

semilinear equations | global existence | damped waves | critical exponent | propagation speed | scale‐invariant | effective damping | scale-invariant | MATHEMATICS, APPLIED | R-N | BLOW-UP | Eulers equations | Damping | Decay rate | Thresholds | Sobolev space | Mathematical analysis | Estimates | Energy of solution | Cauchy problem

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 09/2012, Volume 75, Issue 14, pp. 5723 - 5735

This note deals with the strongly damped nonlinear wave equation utt−Δut−Δu+f(ut)+g(u)=h with Dirichlet boundary conditions, where both the nonlinearities f...

Global and exponential attractors | Strongly damped wave equation | Regularity | Critical nonlinearity | MATHEMATICS | MATHEMATICS, APPLIED | DEFORMABLE MEDIA | EXPONENTIAL ATTRACTORS | CONSTRUCTION | UNIFIED PROCEDURE

Global and exponential attractors | Strongly damped wave equation | Regularity | Critical nonlinearity | MATHEMATICS | MATHEMATICS, APPLIED | DEFORMABLE MEDIA | EXPONENTIAL ATTRACTORS | CONSTRUCTION | UNIFIED PROCEDURE

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2013, Volume 2013, Issue 1, pp. 1 - 11

In this paper, the local fractional variational iteration method is given to handle the damped wave equation and dissipative wave equation in fractal strings....

local fractional variational iteration method | Mathematical and Computational Biology | local fractional operators | Analysis | damped wave equation | Mathematics, general | Mathematics | Applications of Mathematics | Topology | dissipative wave equation | fractal strings | Differential Geometry | Damped wave equation | Fractal strings | Local fractional operators | Dissipative wave equation | Local fractional variational iteration method | DECOMPOSITION METHOD | TIME | HOMOTOPY PERTURBATION METHOD | MATHEMATICS | VARIABLE-COEFFICIENTS | EXP-FUNCTION METHOD | MEDIA | DIFFUSION | NONLINEAR-WAVE | Discrete-time systems | Usage | Innovations | Wave functions | Iterative methods (Mathematics) | Methods | Quantum theory

local fractional variational iteration method | Mathematical and Computational Biology | local fractional operators | Analysis | damped wave equation | Mathematics, general | Mathematics | Applications of Mathematics | Topology | dissipative wave equation | fractal strings | Differential Geometry | Damped wave equation | Fractal strings | Local fractional operators | Dissipative wave equation | Local fractional variational iteration method | DECOMPOSITION METHOD | TIME | HOMOTOPY PERTURBATION METHOD | MATHEMATICS | VARIABLE-COEFFICIENTS | EXP-FUNCTION METHOD | MEDIA | DIFFUSION | NONLINEAR-WAVE | Discrete-time systems | Usage | Innovations | Wave functions | Iterative methods (Mathematics) | Methods | Quantum theory

Journal Article

Complex Variables and Elliptic Equations, ISSN 1747-6933, 08/2018, Volume 63, Issue 7-8, pp. 931 - 944

The paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for strongly damped nonlinear wave...

strongly damped Kirchhoff equation | determining functionals | Strongly damped wave equation | finite-dimensional behavior | BEHAVIOR | GLOBAL ATTRACTORS | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | REGULARITY | NAVIER-STOKES | DYNAMICS | FREEDOM | DISSIPATIVE SYSTEMS

strongly damped Kirchhoff equation | determining functionals | Strongly damped wave equation | finite-dimensional behavior | BEHAVIOR | GLOBAL ATTRACTORS | MATHEMATICS | PARTIAL-DIFFERENTIAL-EQUATIONS | REGULARITY | NAVIER-STOKES | DYNAMICS | FREEDOM | DISSIPATIVE SYSTEMS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 05/2019, Volume 182, pp. 209 - 225

We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem...

Three space dimensions | Lifespan | Semilinear damped wave equation | Blow-up | MATHEMATICS | LIFE-SPAN | MATHEMATICS, APPLIED | Boundary value problems | Life span | Mathematical analysis | Wave equations

Three space dimensions | Lifespan | Semilinear damped wave equation | Blow-up | MATHEMATICS | LIFE-SPAN | MATHEMATICS, APPLIED | Boundary value problems | Life span | Mathematical analysis | Wave equations

Journal Article