Related papers: Initial boundary value problem for a strongly damp…
This paper is devoted to the lifespan of solutions to a damped fourth-order wave equation with logarithmic nonlinearity $$u_{tt}+\Delta^2u-\Delta u-\omega\Delta u_t+\alpha(t)u_t=|u|^{p-2}u\ln|u|.$$ Finite time blow-up criteria for solutions…
We discuss several classes of linear second order initial-boundary value problems, where damping terms appear in the main wave equation as well as in the dynamic boundary condition. We investigate their well-posedness and describe some…
In this work, we investigate the influence of general damping and potential terms on the blow-up and lifespan estimates for energy solutions to power-type semilinear wave equations. The space-dependent damping and potential functions are…
In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…
In this paper, we give a small data blow-up result for the one-dimensional semilinear wave equation with damping depending on time and space variables. We show that if the damping term can be regarded as perturbation, that is, non-effective…
This article studies the finite time blow-up of weak solutions to a structural acoustics model consisting of a semilinear wave equation defined on a bounded domain $\Omega\subset\mathbb{R}^3$ which is strongly coupled with a Berger plate…
In this paper, we study a semilinear weakly coupled system of wave equations with power nonlinearities. More precisely, we couple (through the nonlinear terms) a wave equation and a damped wave equation with a time-dependent coefficient for…
In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we…
In this work, we investigate the problem of finite time blow up as well as the upper bound estimates of lifespan for solutions to small-amplitude semilinear wave equations with mixed nonlinearities $a |u_t|^p+b |u|^q$, posed on…
In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear…
A weak formulation for the so-called "semilinear strongly damped wave equation with constraint" is introduced and a corresponding notion of solution is defined. The main idea in this approach consists in the use of duality techniques in…
This paper is devoted to study a nonlinear wave equation with boundary conditions of two-point type. First, we state two local existence theorems and under suitable conditions, we prove that any weak solutions with negative initial energy…
In this paper we prove the blow-up theorem in the critical case for weakly coupled systems of semilinear wave equations in high dimensions. The upper bound of the lifespan of the solution is precisely clarified.
In this paper, we investigate the initial boundary value problem of the following nonlinear extensible beam equation with nonlinear damping term $$u_{t t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta u_t+\left|u_t\right|^{r-1}…
This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical time-dependent damping term (DW). The result is the sharp upper bound of lifespan of solution with respect to the small…
In this paper, we consider a semilinear system of damped wave equations coupled through power nonlinearities of derivative-type. In particular, we consider a classical damped wave equation, i.e., with constant coefficients, and a wave…
In this paper, we consider the finite time blow-up results for a parabolic equation coupled with superlinear source term and local linear boundary dissipation. Using a concavity argument, we derive the sufficient conditions for the…
This paper concerns estimates of the lifespan of solutions to the semilinear damped wave equation. We give upper estimates of the lifespan for the semilinear damped wave equation with variable coefficients in all space dimensions.
The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data are posed in the energy space. The aim of the paper is to…
This paper studies the upper bound of the lifespan of classical solutions of the initial value problems for one dimensional wave equations with quasilinear terms of space-, or time-derivatives of the unknown function. The results are same…