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WOS:000614070700001 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(.) < q(.) blows up in finite time.

WOS:000754310800004 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.

WOS:000754310800003 We consider a system of viscoelastic equations with degenerate damping and source terms under Dirichlet boundary condition. We prove the exponential growth of solutions under some restrictions on the initial data, relaxation functions and degenerate damping terms

WOS:000754729000004 In this article, we study a plate equation with frictional damping, nonlinear source and time delay. Firstly, we establish the local existence by using the semigroup theory. Then, under suitable conditions, we prove the nonexistence of global solutions for positive initial energy. Time delays often appear in many practical problems such as thermal, economic phenomena, biological, chemical, physical, electrical engineering systems, mechanical applications and medicine.

In this work, we consider a logarithmic m-Laplacian type equation with delay term with initial and boundary conditions. Under suitable conditions on the initial data, we study the nonexistence of solutions in a finite time with negative initial energy $E\left( 0\right)

This paper deals with the initial-boundary value problem for generalized heat equations with variable exponent in a bounded domain. Under suitable conditions, we discuss the lower and upper bounds for the blow up time of solutions.

In this work, we investigate a quasilinear system of two viscoelastic equations with degenarete damping, dispersion and source terms under Dirichlet boundary conditions. Under suitable conditions on the relaxation function $h_{i}$ $\left( i=1,2\right)$ and initial data, we establish global existence and general decay results. This work generalizes and improves earlier results in the literature.

This paper deals with a problem of a wave equation with p-Laplacian and logarithmic nonlinearity term. By the contraction mapping criterion and following the proof lines in [15], we establish the local existence of weak solutions. Finally, under suitable conditions, we present the finite-time blow up of solutions for negative initial energy. .

In this paper, we deal with a nonlinear Timoshenko equation with delay term and variable exponents. Under suitable conditions, we prove the blow-up of solutions in a finite time. Our results are more general than the earlier results. Time delays arise in many applications, for instance, it appears in physical, chemical, biological, thermal and economic phenomena. Also, delay is source of instability, a small delay can destabilize a system which is uniformly asymptotically stable. Several physical phenomena such as flows of electro-rheological fluids or fluids with temperature-dependent viscosity, nonlinear viscoelasticity, filtration processes through a porous media and image processing are modelled by equations with variable exponents.

This work deals with a nonlinear wave equation with delay term and variable exponents. Firstly, we prove the blow up of solutions in a finite time for negative initial energy. After, we obtain the decay results by applying an integral inequality due to Komornik. These results improve and extend earlier results in the literature. Generally, time delays arise in many applications. For instance, it appears in physical, chemical, biological, thermal and economic phenomena. Moreover, delay is source of instability. A small delay can destabilize a system which is uniformly asymptotically stable. Recently, several physical phenomena such as flows of electro-rheological fluids or fluids with temperature-dependent viscosity, nonlinear viscoelasticity, filtration processes through a porous media and image processing are modelled by equations with variable exponents.

We investigate a viscoelastic plate nonlinear system with degenerate damping terms on a bounded domain Rn with Dirichlet boundary conditions. The nonlinearities f1(u; v) and f2(u; v) act as a strong source in the system. Under some restriction on the parameters in the system, we prove the global existence result of weak solution.

In this paper, we consider the initial boundary value problem of a coupled viscoelastic Kirchhoff-type equations with degenerate damping: {u(tt) - M(parallel to del u parallel to(2)) Delta u+ integral(t)(0) mu(1)(t - s) Delta(s)ds + |u|k +|v|l|ut|p-1ut=f1(u,v), vtt-M(parallel to del v parallel to 2) Delta u+ integral(t)(0) mu 2(t - s) increment v(s)ds + |v|theta +|u|rho |vt|q-1vt=f2(u,v). Firstly, we prove a local existence theorem by using the Faedo-Galerkin approximations. Then, we study blow up of solutions when initial energy is positive.

In this paper, we investigated a class of doubly nonlinear parabolic systems with Krichhoff-type.We prove a blow up of solutions with negatif initial energy.

This paper deals with the system of Kirchhoff-type equations with a bounded domain Ω⊂Rⁿ. We prove exponential growth of solutions with negative initial energy. Later, we give some estimates for lower bounds of the blow up time.

In this paper, we investigated the initial boundary problem of a class of doubly nonlinear parabolic systems. We prove exponential growth of solution with negative initial energy.

In this work, we considered asystem of higher-order Kirchhoff type equations with initial and boundaryconditions in a bounded domain. Under suitable conditions, we proved an energydecay result by Nakao's inequality techniques.