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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

This paper investigates the initial boundary value problem for a fractional pseudo-parabolic equation with singular potential. The global existence and blow-up of solutions to the initial boundary value problem are obtained at low initial…

Optimization and Control · Mathematics 2025-04-14 Xiang-kun Shao , Nan-jing Huang , Xue-song Li

In this paper, we study the initial boundary value problem for the two dimensional strong damped wave equation with exponentially growing source and damping terms. We first show the well-posedness of this problem and then prove the…

Analysis of PDEs · Mathematics 2013-07-17 Azer Khanmamedov

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

This paper studies a nonlinear plate equation with internal fractional damping and a time-delay term, driven by a polynomial-type nonlinear source. Such a model arises naturally in the description of viscoelastic and feedback-controlled…

Analysis of PDEs · Mathematics 2026-02-24 Iqra Kanwal , Jianghao Hao , Muhammad Fahim Aslam , Mauricio Sepúlveda-Cortés

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

A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the…

Analysis of PDEs · Mathematics 2015-06-19 Varga Kalantarov , Sergey Zelik

In this note, we prove a blow-up result for the semilinear damped wave equation in a compact Lie group with power nonlinearity $|u|^p$ for any $p>1$, under suitable integral sign assumptions for the initial data, by using an iteration…

Analysis of PDEs · Mathematics 2021-03-15 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 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 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 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

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 initial value problem for nonlinear wave equation with weighted nonlinear terms in one space dimension. Kubo & Osaka & Yazici(2013) studied global solvability of the problem under different conditions on the…

Analysis of PDEs · Mathematics 2014-09-23 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 energy decay and the finite time blow-up of the solution to a viscoelastic wave equation with polynomial nonlinearity and weak damping. We establish explicit and general decay results for the solutions by…

Analysis of PDEs · Mathematics 2025-09-05 Qingqing Peng , Yikan Liu

In this paper, we discuss the global existence of weak solutions to the semilinear damped wave equation \begin{equation*} \begin{cases} \partial_t^2u-\Delta u + \partial_tu = f(u) & \text{in}\ \Omega\times (0,T), \\ u=0 & \text{on}\…

Analysis of PDEs · Mathematics 2019-12-03 Motohiro Sobajima

In this article we will investigate the large time behavior of solutions of a special class of initial/boundary value problems that involve nonlinear damped beam equations. We will show that the solution energies of global pseudo classical…

Analysis of PDEs · Mathematics 2025-11-04 David Raske

We consider initial value problem for semilinear damped wave equations in three space dimensions. We show the small data global existence for the problem without the spherically symmetric assumption and obtain the sharp lifespan of the…

Analysis of PDEs · Mathematics 2018-12-18 Masakazu Kato , Miku Sakuraba

In our previous two works, we studied the blow-up and lifespan estimates for damped wave equations with a power nonlinearity of the solution or its derivative, with scattering damping independently. In this work, we are devoted to…

Analysis of PDEs · Mathematics 2019-05-20 Ning-An Lai , Hiroyuki Takamura