相关论文: Lifespan estimates for 1d damped wave equation wit…
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Introducing an appropriate Lyaponuv function, we prove that when the damping is linear, we can find initial…
In this paper, we investigate the long-time behavior of the $L^2$-norm of solutions to the Cauchy problem for the strongly damped wave equation on $\mathbb{R}^n$, with particular focus on the low-dimensional cases $n=1$ and $n=2$. Although…
This paper is devoted to a proof of the conjecture in Takamura(2015) on the lower bound of the lifespan of solutions to semilinear wave equations in two space dimensions. The result is divided into two cases according to the total integral…
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 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…
A semilinear wave equation with slowly varying wave speed is considered in one to three space dimensions on a bounded interval, a rectangle or a box, respectively. It is shown that the action, which is the harmonic energy divided by the…
In this paper we consider the long time behavior of solutions of the initial value problem for the damped wave equation of the form \begin{eqnarray*} u_{tt}-\rho(x)^{-1}\Delta u+u_t+m^2u=f(u) \end{eqnarray*} with some $\rho(x)$ and $f(u)$…
In this paper, we study semilinear damped equations $u_{tt}+u_t-\Delta u=|u|^p$ with the initial data in $({\dot{H}^{-\gamma}}\cap H^s)\times({\dot{H}^{-\gamma}}\cap L^2)$. Chen-Reissig (2023) studied the case $0<\gamma<\frac{n}{2}$ and…
In this paper, we study the blow-up of solutions for semilinear wave equations with scale-invariant dissipation and mass in the case in which the model is somehow 'wave-like'. A Strauss type critical exponent is determined as the upper…
The blow up problem of the semilinear scale-invariant damping wave equation with critical Strauss type exponent is investigated. The life span is shown to be: $T(\varepsilon)\leq C\exp(\varepsilon^{-2p(p-1)})$ when $p=p_S(n+\mu)$ for…
In this paper, we deal with the initial value fractional damped wave equation on $G$, a compact Lie group, with power-type nonlinearity. The aim of this manuscript is twofold. First, using the Fourier analysis on compact Lie groups, we…
In this paper, we study the Cauchy problem of the fractional wave equation with time-dependent damping and the source nonlinearity $f(u)\approx |u|^p$: $$ \begin{cases} \partial_t^2u(t,x)+(-\Delta)^{\sigma/2} u(t,x)+b(t) \partial_t u(t,x)…
A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also…
In this note we analyze the large time behavior of solutions to an initial/boundary problem involving a damped nonlinear beam equation. We show that under physically realistic conditions on the nonlinear terms in the equation of motion the…
In this note, we prove a blow-up result for the semilinear damped wave equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$, under suitable integral sign assumptions for the initial data, by using an iteration…
In this paper, we investigate the blow-up in finite time and the corresponding lifespan estimates for a weakly coupled system of wave equations on a compact Lie group. In particular, we show how the Cauchy data and the presence of lower…
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…
In the present paper, we investigate blow-up and lifespan estimates for a class of semilinear hyperbolic coupled system in $\mathbb{R}^n$ with $n\geqslant 1$, which is part of the so-called Nakao's type problem weakly coupled a semilinear…
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…
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…