Related papers: Remarks on global solutions for nonlinear wave equ…

This paper is devoted to the proof of a global existence result for the water waves equation with smooth, small, and decaying at infinity Cauchy data. We obtain moreover an asymptotic description in physical coordinates of the solution,…

We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence…

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…

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…

We consider the Cauchy problem for the defocusing power type nonlinear wave equation in $(1+3)$-dimensions for energy subcritical powers $p$ in the range $3 < p< 5$. We prove that any solution is global-in-time and scatters to free waves in…

In this paper, the existence, the uniqueness and estimates of solution to the integral Cauchy problem for linear and nonlinear abstract wave equations are proved. The equation includes a linear operator A defined in a Banach space E, in…

In this paper, we show almost global existence of small solutions to the Cauchy problem for symmetric system of wave equations with quadratic (in 3D) or cubic (in 2D) nonlinear terms and multiple propagation speeds. To measure the size of…

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…

The aim of this article is to prove an "almost" global existence result for some semilinear wave equations in the plane outside a bounded convex obstacle with the Neumann boundary condition.

This article concerns the time growth of Sobolev norms of classical solutions to the 3D quasi-linear wave equations with the null condition.

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].…

We study the existence of global solutions to semilinear wave equations on exterior domains $\mathbb{R}^n\setminus\mathcal{K}$, $n\geq2$, with small initial data and nonlinear terms $F(\partial u)$ where $F\in C^\kappa$ and…

It is well-known that in dimensions at least three semilinear wave equations with null conditions admit global solutions for small initial data. It is also known that in dimension two such result still holds for a certain class of…

In this paper, we study the initial boundary value problem for the nonlinear wave equation with combined power-type nonlinearities with variable coefficients. The global behavior of the solutions with non-positive and sub-critical energy is…

We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…

Here we prove a global existence theorem for the solutions of the semi-linear wave equation with critical non-linearity admitting a positive definite Hamiltonian. Formulating a parametrix for the wave equation in a globally hyperbolic…

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…

We study two-dimensional semilinear strongly damped wave equation with mixed nonlinearity $|u|^p+|u_t|^q$ in an exterior domain, where $p,q>1$. Assuming the smallness of initial data in exponentially weighted spaces and some conditions on…

In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…

We study the global existence of solutions to semilinear wave equations with power-type nonlinearity and general lower order terms on $n$ dimensional nontrapping asymptotically Euclidean manifolds, when $n=3, 4$. In addition, we prove…