[PDF] Top 20 On the decay and blow up of solutions for a quasilinear hyperbolic equations with nonlinear damping and source terms

... studied decay of solutions of the problem (), using the techniques combination of the perturbed energy and potential well ...energy decay rates of the solutions, by utilizing the multiplier ... See full document

... The decay estimates of the solution are established by using Nakao’s ...the blow-up of the solution in finite time with neg- ative initial energy, using the technique of appropriate modification for ... See full document

... the decay is polynomially otherwise. For more decay results, we refer the reader to [5, 6, 7, 10, 16, 19, 25, 26, 40, 43, 47, 48] and the references ...for blow-up ...for blow-up ... See full document

... This paper is organized as follows. In Sect. 2, we give material needed for our work. In Sect. 3, we prove the global existence. In Sect. 4, we present some technical lemmas needed in the proof of our result. Section 5 ... See full document

... and blow up of the solution of problem ...the blow up result obtained in [] for a large class of initial data in positive initial energy using some techniques as in Payne and Sattinger [] ... See full document

... the blow-up of solutions for the quasilinear viscoelastic wave equa- tion with strong damping and boundary nonlinear ...with nonlinear boundary damp- ing. But as far as we ... See full document

... time blow- up of solutions for low initial energy or arbitrarily high initial ...linear damping term is replaced by nonlinear damping term in equation ...uniform decay ... See full document

... linear damping ( m = 2 ) and nonlinear source has been first considered by Levine [7] ...that solutions with negative initial energy blew up in fi- nite ...the nonlinear ... See full document

... explicit decay rate estimate of the energy by making use of the perturbed energy method introduced by Cavalcanti et ...time blow up result of the solutions is investigated under certain ... 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

... blows up in finite time if r > p and the initial energy is nonnegative, and gave the decay estimates of the energy function and the lifespan of ... See full document

... blows up with posi- tive probability or it is explosive in energy sense for p > ...stochastic quasilinear viscoelastic wave equation (1.1) can blow up with positive probability or it is ... See full document

... a quasilinear wave equation with acoustic bound- ary ...existence, blow-up and decay of solutions for viscoelastic wave equations with acoustic boundary ...the ... See full document

... with Dirichlet boundary condition, where ρ > , γ ≥ , p ≥ , b = . An exponential decay result for γ >  and b =  has been obtained. For γ =  and b > , Messaoudi and Tatar [, ] showed that there ... See full document

... r > 0, and proved a global existence result for g ≥ 0 and an exponential decay for g > 0. This result has been extended by Messaoudi and Tatar [2,7] to the situation where g = 0 and exponential and ... See full document

... In the present paper, we study the existence and uniqueness of the global weak solution for the initial boundary value problem (1.1)–(1.3). And then we focus on finding sufficient conditions yielding nonexistence of a ... See full document

... the source term makes the problem more ...ponential decay to the solution of Problem (1) with the assumption that the kernel g is of exponential decay and m = 2 (a localized damping mechanism ... See full document

... where a, l > 0 and Ω is a bounded domain in R N (N ≥ 1) with smooth boundary ∂Ω . There have been many articles dealing with properties of solutions to degenerate parabolic equations with homogeneous ... See full document

... like blow-up and global solvability for nonlinear evolu- tion equations have been investigated extensively by many ...parabolic equations with a gradient term, we refer to [–] ... See full document

... a source term with exponential growth at infinity to be specified later, h( · ) is a monotone continuous function with polynomial growth at infinity and with no restriction on the growth rate near the ...exponential ... See full document