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

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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…

Analysis of PDEs · Mathematics 2025-10-22 Yuequn Li , Alessandro Palmieri

In this paper, we study a semilinear weakly coupled system of wave equations with power nonlinearities. More precisely, we couple (through the nonlinear terms) a wave equation and a damped wave equation with a time-dependent coefficient for…

Analysis of PDEs · Mathematics 2025-10-21 Yuequn Li , Alessandro Palmieri

In this paper, we consider blow-up behavior of weak solutions to a weakly coupled system for a semilinear damped wave equation and a semilinear wave equation in $\mathbb{R}^n$. This problem is part of the so-called Nakao's problem proposed…

Analysis of PDEs · Mathematics 2020-11-17 Wenhui Chen , Michael Reissig

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 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 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

We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms.…

Analysis of PDEs · Mathematics 2024-09-04 Mohamed Fahmi Ben Hassen , Makram Hamouda , Mohamed Ali Hamza

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 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

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

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 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

In this paper, we would like to study the weakly coupled system of semilinear structurally damped wave equations with moduli of continuity in nonlinear terms whose powers belong to the critical curve in the $p-q$ plane. Our main purpose is…

Analysis of PDEs · Mathematics 2026-04-09 Trung Loc Tang , Tuan Anh Dao , The Anh Cung

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

In this note we try to understand the blow-up of solutions to Nakao's problem by using nonlinear ordinary differential inequalities.

Analysis of PDEs · Mathematics 2019-04-11 Wenhui Chen , Michael Reissig

In this paper we consider the blow-up of solutions to a weakly coupled system of semilinear damped wave equations in the scattering case with nonlinearities of mixed type, namely, in one equation a power nonlinearity and in the other a…

Analysis of PDEs · Mathematics 2020-11-03 Alessandro Palmieri , Hiroyuki Takamura

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…

Analysis of PDEs · Mathematics 2018-02-28 Zijin Li , Xinghong Pan

An improvement of [18] on the blow-up region and the lifespan estimate of a weakly coupled system of wave equations with damping and mass in the scale-invariant case and with time-derivative nonlinearity is obtained in this article. Indeed,…

Analysis of PDEs · Mathematics 2022-03-29 Makram Hamouda , Mohamed Ali Hamza

In this paper, we consider the initial-boundary value problems with several fundamental boundary conditions (the Dirichlet/Neumann/Robin boundary condition) for the multi-component system of semi-linear classical damped wave equations…

Analysis of PDEs · Mathematics 2022-01-25 Tuan Anh Dao , Masahiro Ikeda
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