[PDF] Top 20 Global solutions to a class of nonlinear damped wave operator equations

... proved global existence of solutions for semilinear damped wave equations in R N with noncompactly supported initial data or in the energy space, in where the nonlinear term f(u) ... See full document

... Brenner and von Wahl 20 proved the existence and uniqueness of classical solutions to the initial boundary problem for 1.1 in Hilbert space. Pecher 21 investigated the existence and uniqueness of Cauchy problem ... See full document

... the nonlinear term. This class contains problem ...obtain global existence, the authors of [1] used the Galerkin ap- proximation method and the monotonicity method (see ...weak solutions to a ... See full document

... ferential equations is that of Quintanilla ...transient solutions of the damped wave equation and established a spatial decay estimate of the kind described by Knowles [10] for the heat ... See full document

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

... 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

... H  H  that completely deter- mines asymptotic behavior of solutions to the strongly damped nonlinear wave equations. In [4] Chueshov pre- sented the approach of a set of determining ... See full document

... In this study, several compact finite difference schemes are developed for solving the generalized NLSE with wave operator (1.1). It is shown that the fully discrete numerical methods conserve the discrete ... See full document

... strong) solutions, and the topological structure of solutions set of strongly damped semilinear wave ...of class r and gave some ... See full document

... for α > , β ≥ , g is a positive summable kernel, H be a real Hilbert space and the operator A : D(A) → H be a self-adjoint linear positive definite operator with domain D(A) ⊂ H such that the embedding ... See full document

... the global existence and blow up of the solution of problem ...large class of initial data in positive initial energy using some techniques as in Payne and Sattinger [] and some estimates used firstly by ... See full document

... quasilinear wave equation with acoustic bound- ary ...the global existence and regularity of the linear ...of solutions for viscoelastic wave equations with acoustic boundary ...blow-up ... See full document

... constant. The nonlinear term f (u) is a smooth function with f (u) = O(u  ) for u → . Equation (.) is reduced to the classical Cahn-Hilliard equation if a =  (see []), which has been widely studied by many ... See full document

... of solutions of ...the global existence of a unique solution un- der the assumptions that the initial data {u 0 ,u 1 } are sufficiently small and u o = ... See full document

... hyper-Bessel operator and es- tablished the series solution by considering both direct and inverse source problem in a rectangular ...differential operator. The explicit solutions of these ... 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

... Travelling wave solutions for a class of nonlinear fourth order variant of a generalized Camassa-Holm equation, ...Travelling wave solutions for a class of generalized kdv ... See full document

... We prove the existence of a solution to the periodic nonlinear second-order ordinary differential equation with damping u x r xu x gx, ux fx, u0 uT, u 0 u T . We suppose that 0 T r x dx 0, the nonlinearity g ... See full document

... Remark . From the proof of Theorem ., we see that the restriction in Theorem . to p, q, and R may extend to small functions.. In fact, it is easy to find that the conclusion is vali[r] ... See full document