English
Related papers

Related papers: Blow-up and lifespan estimates for Nakao's type pr…

200 papers

In this work, we study the blow up results to power-type semilinear wave equation in the high dimensional Schwarzschild spacetime, with damping and potential terms. We can obtain the upper bound estimates of lifespan without the assumption…

Analysis of PDEs · Mathematics 2023-08-04 Mengliang Liu , Mengyun Liu

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…

Analysis of PDEs · Mathematics 2019-12-06 Mengyun Liu , Chengbo Wang

In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be…

Analysis of PDEs · Mathematics 2019-12-06 Mengyun Liu , Chengbo Wang

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…

Analysis of PDEs · Mathematics 2017-09-14 Masahiro Ikeda , Motohiro Sobajima

We give sufficient conditions on the initial data so that a semilinear wave inequality blows-up in finite time. Our method is based on the study of an associated second order differential inequality. The same method is applied to some…

Mathematical Physics · Physics 2007-05-23 M. Jazar , R. Kiwan

In this paper we consider the blow-up for solutions to a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the…

Analysis of PDEs · Mathematics 2019-12-16 Alessandro Palmieri , Hiroyuki Takamura

In this paper, we consider a blow-up solution for the complex-valued semilinear wave equation with power nonlinearity in one space dimension. We first characterize all the solutions of the associated stationary problem as a two-parameter…

Analysis of PDEs · Mathematics 2014-04-25 Asma Azaiez

This paper is concerned with the blowup phenomena for initial value problem of semilinear wave equation with critical space-dependent damping term (DW:$V$). The main result of the present paper is to give a solution of the problem and to…

Analysis of PDEs · Mathematics 2017-09-14 Masahiro Ikeda , Motohiro Sobajima

In our recent precious work, we established the finite time blow up result and upper bound of lifespan estimate to the singular Cauchy problem of semilinear Euler-Poisson-Darboux equation in R^n with subcritical power type nonlinearity. By…

Analysis of PDEs · Mathematics 2026-03-27 Mengting Fan , Ning-An Lai , Hiroyuki Takamura

The article is devoted to investigating the initial boundary value problem for the damped wave equation in the scale-invariant case with time-dependent speed of propagation on the exterior domain. By presenting suitable multipliers and…

Analysis of PDEs · Mathematics 2023-11-28 Makram Hamouda , Mohamed Ali Hamza , Bouthaina Yousfi

In this paper, we consider a weakly coupled system of a wave and damped Klein-Gordon equation with nonlinearities of derivative type. We prove a blow-up result for the Cauchy problem associated with this system for nonnegative and compactly…

Analysis of PDEs · Mathematics 2022-10-28 Alessandro Palmieri , Hiroyuki Takamura

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…

Analysis of PDEs · Mathematics 2026-05-11 Ning-An Lai , Cui Ren , Takiko Sasaki , Hiroyuki Takamura

We consider the initial-boundary value problem of semilinear wave equation with nonlinearity $|u|^p$ in exterior domain in $\mathbf{R}^N$ $(N\geq 3)$. Especially, the lifespan of blowup solutions with small initial data are studied. The…

Analysis of PDEs · Mathematics 2018-12-24 Motohiro Sobajima , Kyouhei Wakasa

We study in this paper the small data Cauchy problem for the semilinear generalized Tricomi equations with a nonlinear term of derivative type $u_{tt}-t^{2m}\Delta u=|u_t|^p$ for $m\ge0$. Blow-up result and lifespan estimate from above are…

Analysis of PDEs · Mathematics 2022-05-23 Ning-An Lai , Nico Michele Schiavone

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…

Analysis of PDEs · Mathematics 2020-10-12 Wei Dai , Hideo Kubo , Motohiro Sobajima

We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in $H^{1}_{loc}\times L^2_{loc}$ or some times in $ W^{1,\infty}\times…

Analysis of PDEs · Mathematics 2016-01-22 Asma Azaiez , Nader Masmoudi , Hatem Zaag

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…

Analysis of PDEs · Mathematics 2022-04-21 Ahmad Z. Fino , Mohamed Ali Hamza

In this work we study the blow-up of solutions of a weakly coupled system of damped semilinear wave equations in the scattering case with power nonlinearities. We apply an iteration method to study both the subcritical case and the critical…

Analysis of PDEs · Mathematics 2019-08-08 Alessandro Palmieri , Hiroyuki Takamura

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 time dependent damping and potential, and mixed nonlinearities…

Analysis of PDEs · Mathematics 2021-04-21 Mengyun Liu

The paper investigates a class of a semilinear wave equation with time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$ in the blow-up…

Analysis of PDEs · Mathematics 2021-11-03 Ahmad Z. Fino , Mohamed Hamza