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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
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
Journal Article
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
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
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
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
Journal Article
International Journal of Computational Methods, ISSN 0219-8762, 02/2019, Volume 16, Issue 1
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
Journal Article
International Journal of Control, ISSN 0020-7179, 11/2019, Volume 92, Issue 11, pp. 2484 - 2498
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
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
Journal Article
Numerische Mathematik, ISSN 0029-599X, 7/2013, Volume 124, Issue 3, pp. 559 - 601
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 03/2007, Volume 17, Issue 3, pp. 411 - 437
Journal Article
Numerical Functional Analysis and Optimization, ISSN 0163-0563, 04/2017, Volume 38, Issue 4, pp. 466 - 485
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
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
Journal Article
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