[PDF] Top 20 On the Strongly Damped Wave Equations with Critical Nonlinearities

... By choosing suitable  0 −I  state spaces, we prove sectorial property of the operator matrix  together with its θ A ηA  adjoint operator, investigate the associated interpolation a[r] ... See full document

... quasilinear wave equation with strong damping, which has many ap- ...the strongly damped wave equations have been extensively studied by many authors ...for strongly ... See full document

... boundedness, classical (resp., strong) solutions, and the topological structure of solutions set of strongly damped semilinear wave equations. Recently, Xia et al. in [22] introduced and ... See full document

... nonlinear wave equations with Dirichlet boundary conditions and periodic conditions with a superquadratic nonlinear terms at infinity which have continuous ...the critical point theory which is the ... See full document

... quasilinear equations because the quasilinear term makes it impossible to find a suitable space in which the corresponding functional possesses both smooth- ness and compactness ...standing wave solutions ... See full document

... u x = u x u x = u x (8) where u u x t = ( ) , is the real function on U × [ 0, +∞ ) , α > 0 is the strong damping coefficient, β > 0 is the damping coefficient, and K > 0 is the dis- sipation coefficient. In ... See full document

... u + −∆ u + φ ∇ u −∆ u g u + = f x . (1.4) There are many researches on inertial manifolds for nonlinear wave equations (see [5] [6]). Concerning the inertial manifold, many difficulties are solved. So we ... See full document

... value of – on H   (), Webb first considered the asymptotic behavior of strongly damped wave equations in []. Then, in [], Carvalho et al. showed the existence of the global at- tractor for ... See full document

... d φ θ ω t − B  θ ω − B ω → t → +∞ (4.30) which implies that { B ( ) ω } is a random compact attracting set for Φ . It follows from Equations (4.13) and (4.26) that { B ( ) ω } is tempered. Thus by Theorem 2.3, ... See full document

... [14] M. H. Yang, J. Q. Duan and P. Kloeden, “Asymptotic Behavior of Solutions for Random Wave Equations with Nonliear Damping and White Noise,” Nonlinear Analysis: Real World Applications, Vol. 12, No. 1, ... See full document

... by strongly damped wave equations of non-degenerate Kirchhoff type modelling the nonlinear vibrations of an elastic string, and they obtained a precise estimate of upper bound of Hausdorff ... See full document

... Global Solvability of Boundary Value Problem for a Class of Quasilinear Hyperbolic Equations, Sib.. On The Strongly Damped Wave Equation u" Au Au’ + Fu O, SIAMJ.[r] ... See full document

... the classical theory concerning the existence and uniqueness of the solutions of evolution differential equations (cf. []), we have the following lemma (see [] for details). Lemma . Consider the initial value ... See full document

... Equation (1.1) has its origin in the nonlinear vibrations of an elastic string (cf. Narasimha [6]). We call equation (1.1) a nondegenerate equation when α > 0 and β > 0 and a degenerate one when α = 0 and β > 0. ... See full document

... In this paper, we study the existence of exponential attractors for strongly damped wave equa- tions with a time-dependent driving force. To this end, the uniform Hölder continuity is estab- lished ... See full document

... differential equations with damping or distributed deviating arguments have become an important area of research due to the fact that such equations arise in many real life prob- lems; see the research ... See full document

... Theoretically and numerically of periodic oscillations in for suspension bridge model have attracted much attention [5, 9–11]. McKenna and Walter [12] first studied large- amplitude periodic oscillations for a single ... See full document

... weakly damped nonlinear wave Equation (2) as α, ε = 0 is studied in Temam [1] and Zhu [2] and Wang [3] and the one for the strongly damped nonlinear wave equation is considered in Zhou ... See full document

... Ikehata, On global solutions and energy decay for the wave equations of the Kirchhoff type with nonlinear damping terms, J.. Messaoudi, Blow up in a nonlinearly damped wave equation, Mat[r] ... See full document

... Kirchhoff wave equation with strong nonlinear damping was still well-posed and the related evolution semigroup had a fi- nite-dimensional global attractor in 1 1 ... See full document