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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 consider the semi-linear wave systems with power-nonlinearities and space-dependent dampings and potentials. We obtain the blow-up regions for three types wave systems as well as the lifespan estimates.

Analysis of PDEs · Mathematics 2026-01-14 Mengliang Liu

In this paper, we consider the semi-linear wave systems with power-nonlinearities and a large class of space-dependent damping and potential. We obtain the same blow-up regions and the lifespan estimates for three types wave systems,…

Analysis of PDEs · Mathematics 2022-11-22 Mengliang Liu

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,…

Analysis of PDEs · Mathematics 2021-01-19 Ning-An Lai , Nico Michele Schiavone , 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 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 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 time dependent damping and potential, and mixed nonlinearities…

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

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

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

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.

Analysis of PDEs · Mathematics 2015-08-21 Masahiro Ikeda , Yuta Wakasugi

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…

Analysis of PDEs · Mathematics 2015-08-21 Yuta Wakasugi

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

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 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.

Analysis of PDEs · Mathematics 2014-04-22 Yuki Kurokawa , Hiroyuki Takamura , Kyouhei Wakasa

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

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

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

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…

Analysis of PDEs · Mathematics 2018-12-19 Alessandro Palmieri , Ziheng Tu
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