相关论文: Global existence for a quasilinear wave equation o…

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…

The authors show that bilinear estimates for null forms hold for Dirichlet-wave equations outside of convex obstacle. This generalizes results for the Euclidean case of Klainerman and Machedon, and of Sogge for the variable coefficient…

We prove small-data global existence to semi-linear wave equations on hyperbolic space of dimension greater than or equal to three, for nonlinearities that have the form of a sufficiently high integer power of the solution. We also prove…

In the significant work of [2], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [22].…

The global existence for semilinear wave equations with space-dependent critical damping $\partial_t^2u-\Delta u+\frac{V_0}{|x|}\partial_t u=f(u)$ in an exterior domain is dealt with, where $f(u)=|u|^{p-1}u$ and $f(u)=|u|^p$ are in mind.…

The paper is devoted to investigating long time behavior of smooth small data solutions to 3-D quasilinear wave equations outside of compact convex obstacles with Neumann boundary conditions.

In this paper we prove global and almost global existence theorems for nonlinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides. We can handle both the case of Dirichlet boundary conditions and Neumann…

We show that a general class of quasilinear wave equations have global solutions for small initial data as we conjectured in an earlier paper.

In this paper, we prove almost global existence of solutions to certain quasilinear wave equations with quadratic nonlinearities in infinite homogeneous waveguides with Neumann boundary conditions. We use a Galerkin method to expand the…

In this paper, we establish the global existence of a semi-linear class of hyperbolic equations in 3+1 dimensions, that satisfy the bounded weak null condition. We propose a conformal compactification of the future directed null-cone 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 global existence for quasilinear wave equations outside of a wide class of obstacles. The obstacles may contain trapped hyperbolic rays as long as there is local exponential energy decay for the associated linear wave equation.…

In this paper we prove the global existence and uniqueness of the low regularity solutions to the Cauchy problem of quasi-linear wave equations with radial symmetric initial data in three space dimensions. The results are based on the…

We consider the nonlinear Dirac equations in one dimension and review various results on global existence of solutions in H1. Depending on the character of the nonlinear terms, existence of the large-norm solutions can be extended for all…

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…

We prove almost global existence for semilinear wave equations outside of nontrapping obstacles. We use the vector field method, but only use the generators of translations and Euclidean rotations. Our method exploits 1/r decay of wave…

We study the initial-boundary value problem of quasilinear wave equations outside of a star-shaped obstacle in four space dimensions, in which the nonlinear term under consideration may explicitly depend on the unknown function itself. By…

Global existence and scattering for the nonlinear defocusing Schr\"odinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we…

For any subcritical index of regularity $s>3/2$, we prove the almost global well posedness for the 2-dimensional semilinear wave equation with the cubic nonlinearity in the derivatives, when the initial data are small in the Sobolev space…

We solve here the so called division problem for wave equations with generic quadratic non-linearities in high dimensions. Specifically, we show that semilinear wave equations which can be written as systems involving quadratic derivative…