相关论文: Global existence and blow-up for semilinear damped…

In this paper we consider a multi-dimensional damped semiliear wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. We firstly prove the local existence by using the Faedo-Galerkin approximations combined…

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…

H\"ormander proved global existence of solutions for sufficiently small initial data for scalar wave equations in $(1+4)-$dimensions of the form $\Box u = Q(u, u', u'')$ where $Q$ vanishes to second order and $(\partial_u^2 Q)(0,0,0)=0$.…

In this paper, we are concerned with the global existence of small data weak solutions to the $n-$dimensional semilinear wave equation $\partial_t^2u-\Delta u+\frac{\mu}{t}\partial_tu=|u|^p$ with time-dependent scale-invariant damping,…

In this paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…

In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in [M. D'Abbicco, A wave equation with structural damping and…

We study global existence and decay estimates for quasilinear wave equations with dissipative terms in the Sobolev space $H^L \times H^{L-1}$, where $L \geq [d/2]+3$. The linear dissipative terms depend on space variable coefficient, and…

For the $2$-D semilinear wave equation with scale-invariant damping $\partial_t^2u-\Delta u+\frac{\mu}{t}\partial_tu=|u|^p$, where $t\ge 1$ and $p>1$, in the paper [T. Imai, M. Kato, H. Takamura, K. Wakasa, The lifespan of solutions of…

This work presents results on solutions of the one-dimensional damped wave equation, also called telegrapher's equation, when the initial conditions are general distributions, not only functions. We make a complete deduction of its…

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…

The final open part of the famous Strauss conjecture on semilinear wave equations of the form \Box u=|u|^{p}, i.e., blow-up theorem for the critical case in high dimensions was solved by Yordanov and Zhang, or Zhou independently. But the…

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.

In this paper, we study the semilinear wave equation with lower order terms (damping and mass) and with power type nonlinearity $|u|^p$ on compact Lie groups. We will prove the global in time existence of small data solutions in the…

For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result…

This paper studies initial value problems for semilinear wave equations with spatial weights in one space dimension. The lifespan estimates of classical solutions for compactly supported data are established in all the cases of polynomial…

We consider the initial-boundary value problems on $\mathbb{R}^{+}\times \mathbb{R}^{+}$ for one-dimension systems of quasilinear wave equations with null conditions. We show that for homogeneous Dirichlet boundary values and sufficiently…

In this paper, we consider the Cauchy problem for a semilinear damped wave equation with the nonlinear term $|u|^{1+2/n} \mu(|u|)$, where $\mu$ is a modulus of continuity. In recent papers by Ebert,Girardi,Reissig (Math. Ann. 378 (2020))…

In connection with the weak null condition, Alinhac introduced a sufficient condition for global existence of small amplitude solutions to systems of semilinear wave equations in three space dimensions. We introduce a slightly weaker…

In this note, we study the Cauchy problem of the semilinear damped wave equation and our aim is the small data global existence for noncompactly supported initial data. For this problem, Ikehata and Tanizawa [5] introduced the energy method…

We are interested in almost global existence cases in the general theory for nonlinear wave equations, which are caused by critical exponents of nonlinear terms. Such situations can be found in only three cases in the theory, cubic terms in…