English
Related papers

Related papers: Lifespan estimates for local solutions to the semi…

200 papers

We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein-de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we…

Analysis of PDEs · Mathematics 2021-03-15 Alessandro Palmieri

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…

Analysis of PDEs · Mathematics 2022-06-22 Makram Hamouda , Mohamed Ali Hamza , Alessandro Palmieri

In the present paper we prove the blow-up in finite time for local solutions of a semilinear Cauchy problem associated with a wave equation in anti-de Sitter spacetime in the critical case. According to this purpose, we combine an ODI…

Analysis of PDEs · Mathematics 2022-11-23 Alessandro Palmieri , Hiroyuki Takamura

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…

Analysis of PDEs · Mathematics 2021-12-14 Kazumasa Fujiwara , Masahiro Ikeda , Yuta Wakasugi

In this work we derive some blow-up results for semilinear wave equations both in de Sitter and anti-de Sitter spacetimes. By requiring suitable conditions on a time-dependent factor in the nonlinear term, we prove the blow-up in finite…

Analysis of PDEs · Mathematics 2022-06-22 Alessandro Palmieri , Hiroyuki Takamura

In this reviewing paper, we are interested in the proof of estimating the lifespan of classical solutions of semilinear wave equations with the critical exponent from above especially in low space dimensions. There are a few ways to show…

Analysis of PDEs · Mathematics 2025-12-09 Hiroyuki Takamura

We examine the solutions of the semilinear wave equation, and, in particular, of the $\varphi ^p$ model of quantum field theory in the curved space-time. More exactly, for $1< p<4$ we prove that solution of the massless self-interacting…

Mathematical Physics · Physics 2019-12-09 Anahit Galstian , Karen Yagdjian

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

In this paper, we consider the finite time blow up of solutions for the following two kinds of nonlinear wave equations on de Sitter spacetime \begin{eqnarray*} &&\square_g=F(u),\\ &&\square_g=F(\partial_tu,\nabla u). \end{eqnarray*} This…

Analysis of PDEs · Mathematics 2016-11-15 Weiping Yan

In this paper, we are focusing on proofs of a blow-up result for a quadratic semilinear wave equation in two space dimensions. There is a logarithmic loss in estimating the lifespan of a classical solution if the 0th moment of the initial…

Analysis of PDEs · Mathematics 2026-05-11 Masakazu Kato , Hiroyuki Takamura , Kyouhei Wakasa

For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obtained for both critical cases and subcritical cases, for all…

Analysis of PDEs · Mathematics 2024-06-05 Kerun Shao , Hiroyuki Takamura , Chengbo Wang

In this paper, we establish blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime with nonlinearity of derivative type. Our approach is based on the integral representation formula for the solution to…

Analysis of PDEs · Mathematics 2021-07-20 Makram Hamouda , Mohamed Ali Hamza , Alessandro Palmieri

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…

Analysis of PDEs · Mathematics 2021-02-23 Ning-An Lai , Mengyun Liu , Ziheng Tu , Chengbo Wang

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

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

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…

Analysis of PDEs · Mathematics 2021-12-14 Masahiro Ikeda , Motohiro Sobajima , Yuta Wakasugi

In this paper we study blow-up and lifespan estimate for solutions to the Cauchy problem with small data for semilinear wave equations with scattering damping and negative mass term. We show that the negative mass term will play a dominant…

Analysis of PDEs · Mathematics 2021-01-19 Ning-An Lai , Nico Michele Schiavone , Hiroyuki Takamura

We consider the Cauchy-Dirichlet problem for semilinear wave equations in a three space dimensional domain exterior to a bounded and non-trapping obstacle. We obtain a detailed estimate for the lower bound of the lifespan of classical…

Analysis of PDEs · Mathematics 2010-09-08 Soichiro Katayama , Hideo Kubo

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper…

Analysis of PDEs · Mathematics 2021-12-28 Kimitoshi Tsutaya , Yuta Wakasugi

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
‹ Prev 1 2 3 10 Next ›