相关论文: Global existence for semilinear wave equations wit…
By using the Strichartz esitmate and Picard iteration, we prove the subcritical(critical in some cases) global solution in $C_t H_x^s\cap C_t^1 H^{s-1}_x$ with small data for semilinear wave equation with nonlinearity of type $(\partial…
In this paper, we consider exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove global existence of smooth solutions. Similar to the constant coefficients case, we show…
This article focuses on almost global existence for quasilinear wave equations with small initial data in 4-dimensional exterior domains. The nonlinearity is allowed to depend on the solution at the quadratic level as well as its first and…
We prove almost global existence for multiple speed quasilinear wave equations with quadratic nonlinearities in three spatial dimensions. We prove new results both for Minkowski space and also for nonlinear Dirichlet-wave equations outside…
This paper proves global existence and sharp pointwise decay for solutions to nonlinear wave equations satisfying the semilinear null condition, on a class of three-dimensional, asymptotically flat, and notably, non-stationary spacetimes.…
In this work we study the global existence for 3d semilinear wave equation with non-negative potential satisfying generic decay assumptions. In the supercritical case we establish the small data global existence result. The approach is…
We establish global existence in 3+1 dimensions of small-amplitude solutions of quasilinear Dirichlet-wave equations satisfying the null condition outside of star-shapped obstacles.
We study global behavior of radial solutions for the nonlinear wave equation with the focusing energy critical nonlinearity in three and five space dimensions. Assuming that the solution has energy at most slightly more than the ground…
In this paper we prove a sharp global existence result for semilinear wave equations with time-dependent scale-invariant damping terms if the initial data is small. More specifically, we consider Cauchy problem of $\partial_t^2u-\Delta…
This is the first of two papers devoted to the study of the properties of the blow-up surface for the $N$ dimensional semilinear wave equation with subconformal power nonlinearity. In a series of papers, we have clarified the situation in…
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…
We prove the existence of global solutions to the nonlinear wave equation in $\mathbb{R}^{1+3}$ $$\Phi_{tt} - \Delta \Phi \pm \Phi|\Phi|^{p-1} = 0$$ in the energy-supercritical regime $p>5$, for a class of large initial data. Our initial…
In this paper we deal with the exterior problem for a system of nonlinear wave equations in two space dimensions, assuming that the initial data is small and smooth. We establish the same type of lower bound of the lifespan for the problem…
In this paper, we consider the nonlinear Schr\"odinger equation with the super critical power of nonlinearity in the attractive case. We give a sufficient condition and a necessary condition to obtain global or blowing up solutions. These…
Some systems of nonlinear wave equations admit global solutions for all sufficiently small initial data, while others do not. The (classical) null condition guarantees that such a result holds, but it is too strong to capture certain…
In this paper we consider a semilinear parabolic equation with nonlinear and nonlocal boundary condition and nonnegative initial datum. We prove some global existence results. Criteria on this problem which determine whether the solutions…
We show global existence of classical solutions for the nonlinear Nordstr\"om theory with a source term and a cosmological constant under the assumption that the source term is small in an appropriate norm, while in some cases no smallness…
In this paper we prove global existence and global behavior of solutions to quasilinear wave-Klein-Gordon systems in $\mathbb{R}^{1+2}$ with quadratic nonlinearities satisfying the null condition. We consider small, regular and compactly…
We deal with existence and non-existence of non-negative entire solutions that blow-up at infinity for a quasilinear problem depending on a non-negative real parameter. Our main objectives in this paper are to provide far more general…
We consider the Cauchy problem of coupled 3-D wave and Klein-Gordon equations with a quadratic form of nonlinearity. We show global existence under several conditions, including large derivative data for wave equations and the null…