This paper is concerned with the blow-up of certain solutions with positive initial energy to the following quasilinear wave equation: u t t − M N u t Δ p · u + g u t = f u . This work generalizes the blow-up result of solutions with negative initial energy.

<abstract><p>An initial value problem is considered for the nonlinear dissipative wave equation containing the $ p(x) $-bi-Laplacian operator. For this problem, sufficient conditions for the blow-up with nonpositive initial energy of a generalized solution are obtained in finite time where a wide variety of techniques are used.</p></abstract>

In the paper, we consider new stability results of solution to class of coupled damped wave equations with logarithmic sources in ℝ n . We prove a new scenario of stability estimates by introducing a suitable Lyapunov functional combined with some estimates.

Due to the rapid development of algorithms and techniques that are used to deal with mixed integer nonlinear programming (MINLP) problems, many global MINLP solvers were introduced. In this paper, computational experiments were done to compare between the performances of five of these solvers. Some of these solvers do not support trigonometric functions. Therefore, piecewise linear approximation (PLA) is applied to problems having these function so the solvers can deal with these problems. Additional computational tests were performed on to show how PLA can be useful, even to some powerful global solvers.

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