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In this paper, we consider a nonlinear wave equation with damping and source terms of variable-exponent types. First, we use the stable-set method to prove a global result. Then, by applying an integral inequality due to Komornik, we obtain the stability result. [ABSTRACT FROM AUTHOR]

The Riemannian wave equationwith linear lower order termand unspecified behavior of the nonlinear feedback is considered. Using themethod in [LT] we prove that the energy of the solution decays faster than the solution of some associated differential equation. The decay rate of a general second order hyperbolic equation with polynomial growth at the origin off is also discussed. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to study, under a suitable geometric conditions, the indirect boundary stabilization for coupled Schr #x00F6;dinger equations with variable coefficients and one Dirichlet boundary feedback. The polynomial energy decay rate for smooth solutions is obtained by the combination of the Riemannian geometry method in [Ya1] and the ideas of I. Lasiecka and R. Triggiani in [LT3] . [ABSTRACT FROM AUTHOR]

In this paper, we consider a second-order hyperbolic equations with variable coefficients and linear lower-order term. We use a new main multiplier and a suitable nonlinear version of a compactness uniqueness argument (Acta. Math. Sin. – Engl. Ser. 20(6) (2004), 1057–1072) to obtain the exponential stabilization of this system where no condition of smallness is needed. [ABSTRACT FROM AUTHOR]

In this article, we consider a coupled system of two nonlinear hyperbolic equations, where the exponents in the damping and source terms are variables. First, we prove a theorem of existence and uniqueness of weak solution, by using the Faedo Galerkin approximations and the Banach fixed point theorem. Then, using the energy method, we show that certain solutions with positive initial energy blow up in finite time. We also give some numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]