[PDF] Top 20 Decay estimate of solutions for a semi-linear wave equation

... The decay property of the solution operators to ...the linear problem and show the decay ...the decay estimates of solutions for the initial value problem ... See full document

... In this paper, we investigate the Cauchy problem for the generalized damped Bq equation. By applying fixed point theorem, we prove the global existence and asymptotic decay estimate of ... See full document

... uniform decay of solutions provided that the initial data are in same stable ...the solutions with positive initial energy that blow up in finite ... See full document

... exponential decay estimate of global solutions for the initial boundary value problem of the following Kirchhoff-type equation with strong dissipative and source terms in a bounded domain ... See full document

... Spatial decay estimates for several types of partial differential equations and systems have been the subject of extensive investigations in the lit- erature for close to a century and a ...in linear ... See full document

... The rest of this paper is organized as follows. In the next section, we give some def- initions and some propositions of the solutions for the problem (.)-(.). Section  is devoted to giving the propagation ... See full document

... damped wave equations and Marguerre–von Karman system, some en- ergy decay rate estimates were obtained in [11–15, 19, 20] and the references ...the solutions for evolu- tion ... See full document

... Kirchhoff equation and obtained the optimal decay rate estimate of solution ...of wave equation with non- linear boundary damping and source terms, Vitillaro [21] established the ... See full document

... viscoelastic equation for Kirchhoff type con- taining Balakrishnan-Taylor damping with a time-varying delay and acoustic boundary ...tic wave equations with acoustic boundary conditions, we refer the reader ... See full document

... to semi-linear wave equations with damp- ing term have been studied by many researchers( see ...the semi-linear damped wave equation with the forcing ... See full document

... a linear function, whereas the decay is polynomially ...more decay results, we refer the reader to [5, 6, 7, 10, 16, 19, 25, 26, 40, 43, 47, 48] and the references ...the solutions to two ... See full document

... with linear or nonlinear boundary feed- back was investigated by several authors; see, for example, [–] among ...form decay for plates with memory was studied in [–] and the references ...the ... See full document

... of solutions for the PDE system have been studied extensively, and many achievements have been ...existence, decay and blow-up for the last two decades, see ... See full document

... non- linear models of strings, beams, plates, and so ...second-order wave equation and the fourth-order Euler-Bernoulli beam equation ...of wave and plate equations by adding some types ... See full document

... exponential decay rate of the solution under some assumption on g(s) and ...of solutions for the viscoelastic equation, at same time he also obtained a blow-up result with negative ... See full document

... In this paper, we will propose a somewhat different method to find various exact solutions of Equations ((1) & (2)). First of all, a nonlinear transformation from the solution of a linear ... See full document

... Though we consider the conditions on the term involving the gradient are too restrictive and we combine some known ideas to obtain our result, our findings extend those decay results in [22,27] and these findings ... See full document

... where A is a strictly positive self-adjoint linear operator and α > 0, β ≥ 0 and the mem- ory kernel μ is a decreasing function satisfying specific conditions. Subsequently, they established necessary as well as ... See full document

... Linear equation – An equation whose solutions form a straight line on a coordinate plane.. Solutions of a Linear Equation – any point that lies on the line (or) any ordered pair th[r] ... See full document

... for f = g = 0, 0 < x < L, t ≥ 0, where u (x, t) is the lateral displacement, E is the Young modulus, ρ is the mass density, h is the cross-section area, L is the length, ρ 0 is the initial axial tension, δ is the ... See full document