[PDF] Top 20 Existence and general decay estimate for a nonlinear plate problem

... damping coefficient, h is the nonlinear restoring force of the hangers and f is an external force. The well-posedness and long-time behaviour of this problem were proved in [9] under suitable assumptions on ... See full document

... Kirchhoff plate equations in which the boundary (inter- nal) feedback is linear or nonlinear has been studied by several authors, such as Lagnese [1], Komornik [2], Lasiecka [3], Cavalcanti et ...the ... See full document

... concerning existence, nonexistence and long-time behavior of solutions have been ...elliptic problem for p-Laplace operator can be found in ...the existence of a solution for the fractional ... See full document

... global existence theorem and proved that the global solution is uniformly ...by nonlinear damping term in equation ...global existence theorem, uniform decay rate estimate, and ... See full document

... The paper is organized as follows. In Section , we give some preparations for our con- sideration and our main results. In Section , we study an energy decay of the solutions for problem (.). By ... See full document

... value problem for a viscoelastic wave equation with nonlinear boundary damping and internal source ...explicit decay rate estimate of the energy by making use of the perturbed energy ... See full document

... exponential decay for q = 1. But polynomial decay for q > 1 seems to be a harder ...the existence and regularity for station- ary plate equations with transmission conditions similar to ... See full document

... is nonlinear and in the case µ 2 = 0, φ ∼ 1, the problem of existence and energy decay have been previously studied by several authors (see [1, 3, 11, 12, 13]) and many energy estimates have ... See full document

... value problem for a class of nonlinear Kirchhoff-type equations with strong dissipative and source terms u tt   (  u 2 2 )     u a u t b u | |   2 u x ,   , t 0 in a bounded domain, where a b , ... See full document

... value problem of nonlinear viscoelastic plate equations with dissipative ...the decay rate estimate of the energy function is exponential or polynomial depending on the exponents of the ... See full document

... where the memory kernel is a convex decreasing smooth function such that K(0) > K( ∞ ) > 0 and g : R → R is a nonlinear term of at most cubic growth satisfying some conditions. They proved the ... See full document

... sufficiently negative, Messaoudi [29] extended the blow up result of [12] to solutions with negative initial energy only. It worth to mention that, in [14], without considering the relation between m and p, the author ... See full document

... viscoelastic plate equation with a linear time delay ...a general decay result of energy by using suitable energy and Lyapunov ...extensible plate equation with a weak viscoelastic term and a ... See full document

... In this paper, we prove the global existence for the problem (.)-(.) by applying the po- tential well theory introduced by Sattinger [] and Payne and Sattinger []. Meanwhile, we obtain the ... See full document

... in a bounded domain with boundary conditions (1.7)-(1.9). They improved the results of [15] by applying the multiplier techniques. Indeed, they obtained not only a general decay result, but their works also ... See full document

... research existence, uniqueness, and uniform decay of solutions of systems ...of existence and exponential decay when Kirchhoff-type coefficients occur and h 1 ∗ J 1 (Δu), h 2 ∗ J 2 (v) appear as ... See full document

... An important problem in the study of oscillation theory of difference equations is to determine sufficient conditions for all nonoscillatory solutions or all bounded nonoscillatory solution[r] ... See full document

... inhomogeneous norm, and so it lacks the homogeneity property: kf |k|f. However, for nonlinear problems such as 1.3, the homogeneity property may not be an essential factor— we try to explain that the new space ... See full document

... “Singular nonlinear problem for ordinary differential equation of the second-order on the half-line,” in Mathematical Models in Engineering, Biology and Medicine: International Conference on Boundary Value ... See full document

... Remark . The assumptions (A) and (A) have been used in []. The condition (.) is the well-known Ambrosetti-Rabinowitz condition, widely used in elliptic problem. Also as remarked in [, ], the mountain ... See full document