相关论文: Life-span of blowup solutions to semilinear wave e…
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…
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 study the finite-time blow up of solutions to the following semilinear wave equation with time-dependent damping \[ \partial_t^2u-\Delta u+\frac{\mu}{1+t}\partial_tu=|u|^p \] in $\mathbb{R}_{+}\times\mathbb{R}^n$. More…
We consider the Cauchy problem for semilinear wave equations with variable coefficients and time-dependent scattering damping in $\mathbf{R}^n$, where $n\geq 2$. It is expected that the critical exponent will be Strauss' number $p_0(n)$,…
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…
We study a kind of nonlinear wave equations with damping and potential, whose coefficients are both critical in the sense of the scaling and depend only on the spatial variables. Based on the earlier works, one may think there are two kinds…
In this article, we investigate the blow-up for local solutions to a semilinear wave equation in the generalized Einstein - de Sitter spacetime with nonlinearity of derivative type. More precisely, we consider a semilinear damped wave…
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…
The final open part of the famous Strauss conjecture on semilinear wave equations of the form \Box u=|u|^{p}, i.e., blow-up theorem for the critical case in high dimensions was solved by Yordanov and Zhang, or Zhou independently. But the…
The main purpose of the present paper is to study the blow-up problem of the wave equation with space-dependent damping in the \textit{scale-invariant case} and time derivative nonlinearity with small initial data. Under appropriate initial…
The final open part of Strauss' conjecture on semilinear wave equations was the blow-up theorem for the critical case in high dimensions. This problem was solved by Yordanov and Zhang in 2006, or Zhou in 2007 independently. But the estimate…
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.
We concern the blow up problem to the scale invariant damping wave equations with sub-Strauss exponent. This problem has been studied by Lai, Takamura and Wakasa (\cite{Lai17}) and Ikeda and Sobajima \cite{Ikedapre} recently. In present…
We verify the critical case $p=p_0(n)$ of Strauss' conjecture (1981) concerning the blow-up of solutions to semilinear wave equations with variable coefficients in $\mathbf{R}^n$, where $n\geq 2$. The perturbations of Laplace operator are…
We consider the initial value problem for the semilinear wave equation with time-dependent effective damping. The interest is the behavior of lifespan of solutions in view of the asymptotic profile of the damping as $t\to \infty$. The…
We consider the following semilinear wave equation with time-dependent damping. \begin{align} \tag{NLDW} \left\{ \begin{array}{ll} \partial_t^2 u - \Delta u + b(t)\partial_t u = |u|^{p}, & (t,x) \in [0,T) \times \mathbb{R}^n, \\…
We study blow-up behavior of solutions for the Cauchy problem of the semilinear wave equation with time-dependent damping. When the damping is effective, and the nonlinearity is subcritical, we show the blow-up rates and the sharp lifespan…
In this paper we establish blow-up results and lifespan estimates for semilinear wave equations with scattering damping and negative mass term for subcritical power, which is the same as that of the corresponding problem without mass term,…
This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown…
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…