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In this work, we deal with the higher-order hyperbolic-type equation. Firstly, we prove the global existence and blow up of solutions with the subcritical initial energy. Later, we prove the global existence and blow up of solutions with the critical initial energy. [ABSTRACT FROM AUTHOR]

In this paper, we consider the weighted m -biharmonic equation with nonlinear damping and source terms. We proved the global existence of solutions. Later, the decay of the energy is established by using Nakao's inequality. Finally, we proved the blow-up of solutions in finite time. [ABSTRACT FROM AUTHOR]

This paper deals with a hyperbolic-type equation with a logarithmic source term and dynamic boundary condition. Given convenient initial data, we obtained the local existence of a weak solution. Local existence results of solutions are obtained using the Faedo-Galerkin method and the Schauder fixed-point theorem. Additionally, under suitable assumptions on initial data, the lower bound time of the blow-up result is investigated. [ABSTRACT FROM AUTHOR]

In this paper, we deal with a p(x)-biharmonic heat equation with variable exponent under Dirichlet boundary and initial condition. We prove the blow up of solutions under suitable conditions. [ABSTRACT FROM AUTHOR]

In this work, we investigate generalized coupled nonlinear Klein-Gordon equations with nonlinear damping and source terms and initial-boundary value conditions, in a bounded domain. We obtain decay of solutions by use of Nakao inequality. The blow up of solutions with negative initial energy is also established. [ABSTRACT FROM AUTHOR]

In this research, we take into account the Kirchhoff type equation with variable exponent. The Kirchhoff type equation is known as a kind of evolution equations, namely, PDEs, where t is an independent variable. This type problem can be extensively used in many mathematical models of various applied sciences such as flows of electrorheological fluids, thin liquid films, and so on. This research, we investigate the upper bound for blow up time under suitable conditions. [ABSTRACT FROM AUTHOR]

In this work, we analyze the influence of the logarithmic source term on solutions to quasilinear riser equation. Firstly, we prove blow up results. Later, we obtain that solutions are global with negative initial energy. [ABSTRACT FROM AUTHOR]

This article deals with the study of the higher-order Kirchhoff-type equation with delay term in a bounded domain with initial boundary conditions, where firstly, we prove the global existence result of the solution. Then, we discuss the decay of solutions by using Nakao's technique and denote polynomially and exponentially. Furthermore, the blow-up result is established for negative initial energy under appropriate conditions. [ABSTRACT FROM AUTHOR]

This work deals with a Petrovsky equation with delay term and variable exponents. Firstly, we establish the local existence result by the Faedo-Galerkin method. Later, we prove the blow-up of solutions in a finite time. Our results are more general than the earlier results. [ABSTRACT FROM AUTHOR]

A Kirchhoff equation type with memory term competing with a logarithmic source is considered. By using potential well theory, we obtained the global existence of solution for the initial data in a stability set created from Nehari Manifold and prove blow up results for initial data in the instability set. [ABSTRACT FROM AUTHOR]

In this work, we deal with a logarithmic quasilinear hyperbolic equation with delay term. Under suitable conditions, we get blow up of solutions in a finite time. Our results are more general than the earlier results. [ABSTRACT FROM AUTHOR]

This study deals with the parabolic type Kirchhoff equation with logarithmic nonlinearity in a bounded domain. We obtain the finite time blow-up of solutions. This improves and extends some previous studies. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a nonlinear system of viscoelastic equations with degenerate damping and source terms in a bounded domain. Under appropriate assumptions on the parameters, degenerate damping terms and the relaxation functions wi, (i= 1, 2), we prove local existence and uniqueness of the solution by using the Faedo–Galerkin method with a new scenario. Then, we prove the blow-up of weak solutions to problem (1.1). This improves earlier results in the literature [6,23,25]. [ABSTRACT FROM AUTHOR]

In this work, we consider a nonlinear system of viscoelastic equations of Kirchhoff type with degenerate damping and source terms in a bounded domain. Under suitable assumptions on the initial data, the relaxation functions gi(i  =  1,2) and degenerate damping terms, we obtain global existence of solutions. Then, we prove the general decay result. Finally, we prove the finite time blow‐up result of solutions with negative initial energy. This work generalizes and improves earlier results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the following extensible beam equation utt + Δ2u - M (‖∇u‖2) Δu + ∣ut∣p-1 ut = ∣u∣q-1 u with initial and boundary conditions. Under suitable conditions on the initial datum, we prove that the solution blows up in finite time with positive initial-energy. [ABSTRACT FROM AUTHOR]

In this work, we consider coupled nonlinear wave equations with degenerate damping and source terms. We will show the blow up of solutions in finite time with positive initial energy. This improves earlier results in the literature. [ABSTRACT FROM AUTHOR]

In this work we investigate the global existence, decay, and blow up of solutions for a quasilinear hyperbolic equation. We prove the decay estimates of the energy function by using Nakao's inequality. Also, we obtain the blow up of solutions and lifespan estimates in three different ranges of the initial energy. [ABSTRACT FROM AUTHOR]

We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao's inequality. The nonexistence of global solutions is discussed under some conditions on the given parameters. [ABSTRACT FROM AUTHOR]

In this article, we consider a nonlinear plate (or beam) Petrovsky equation with strong damping and source terms with variable exponents. By using the Banach contraction mapping principle we obtain local weak solutions, under suitable assumptions on the variable exponents p(·) and q(·). Then we show that the solution is global if p(·) ≥ q(·). Also, we prove that a solution with negative initial energy and p(·)

In this article, we consider a nonlinear p(x)-Laplacian equation with time delay and variable exponents. Firstly, we prove the blow up of solutions. Then, by applying an integral inequality due to Komornik, we obtain the decay result. [ABSTRACT FROM AUTHOR]