A viscoelastic equation with Balakrishnan-Taylor damping and non-linear boundary/interior sources is considered in a bounded domain. Under appropriate assumptions on the relaxation function and with certain initial data and by adopting the perturbed energy method, we establish uniform decay rate of the solution energy in terms of the behavior of the… (More)
The initial boundary value problem for an integro-differential equation with nonlinear damping in a bounded domain is considered. The local existence and blow-up of solutions with positive initial energy are discussed under some conditions. Estimates of the lifespan of solutions are also given.
Let be a d-dimensional simplex with vertices v 0 ; ; v d and B n (f;) denote the n th degree Bernstein polynomial of a continuous function f on. Dahmen and Micchelli 4] proved that B n (f;) B n+1 (f;); n 2 N; for any convex function f on , and it is clear that a necessary and suucient condition for the inequality to become an identity for all n 2 N is that… (More)