相关论文: John's blow up examples and scattering solutions f…

We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions…

We investigate finite-time blow-up of solutions to the Cauchy problem for a semilinear heat equation posed on infinite graphs. Assuming that the initial datum is sufficiently large, we establish a general blow-up criterion valid on…

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…

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…

The blow-up for semilinear wave equations with the scale invariant damping has been well-studied for sub-Fujita exponent. However, for super-Fujita exponent, there is only one blow-up result which is obtained in 2014 by Wakasugi in the case…

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…

In this paper, we study the semilinear wave equations with the inverse-square potential. By transferring the original equation to a "fractional dimensional" wave equation and analyzing the properties of its fundamental solution, we…

We consider in this paper a large class of perturbed semilinear wave equation with subconformal power nonlinearity. In particular, we allow log perturbations of the main source. We derive a Lyapunov functional in similarity variables and…

In this paper we consider the blow-up for solutions to a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. After introducing suitable functionals proposed by Lai-Takamura for the…

We consider the non linear focusing wave equation $\partial_{tt}u-\Delta u-u|u|^{p-1}=0$ in large dimensions and for radially symmetric data, in the energy supercritical zone for p large enough. We construct finite time blow up solutions…

We consider the Cauchy problem in $\mathbb{R}^n,$ $n\geq 1,$ for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as $t\rightarrow\infty$ of small data solutions have been established in the…

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…

We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in $H^{1}_{loc}\times L^2_{loc}$ or some times in $ W^{1,\infty}\times…

In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence results. We then give some criteria on this problem which determine…

In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity $u_{tt} - \Delta u = u^{p}$ in three space dimensions. We show that for generic large initial…

The problem of blow up of solutions to the initial boundary value problem for non-autonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions of blow up in a…

We present a general construction of semiglobal scattering solutions to quasilinear wave equations in a neighbourhood of spacelike infinity including past and future null infinity, where the scattering data are posed on an ingoing null cone…

We consider the semilinear heat equation, to which we add a nonlinear gradient term, with a critical power. We construct a solution which blows up in finite time. We also give a sharp description of its blow-up profile. The proof relies on…

The final open part of Strauss' conjecture on semilinear wave equations was the blow-up theorem for the critical case in high dimensions. This problem was solved by Yordanov and Zhang in 2006, or Zhou in 2007 independently. But the estimate…

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…