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Nonlinear Analysis, ISSN 0362-546X, 12/2019, Volume 189, p. 111582
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 6944 - 6975
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
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
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
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
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
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
Journal Article
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
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
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
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
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
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
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
Journal Article