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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]

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]