相关论文: Late-time tail for a scalar quasilinear wave equat…
We are interested in the three-dimensional quasilinear wave equations with null condition. Global existence and pointwise decay for this model have been proved in the celebrated works of Klainerman \cite{Klainerman86} and Christodoulou…
We study the asymptotics of solutions to a particular class of systems of linear wave equations, namely, of silent equations. We obtain asymptotic estimates of all orders for the solutions, and show that solutions are uniquely determined by…
We show that the leading-order term in the late-time asymptotics of solutions to the linear wave equation on radially symmetric stationary perturbations of $(2 + 1)$-dimensional Minkowski space is proportional to $u^{-1/2}v^{-1/2}$ (which…
For the Cauchy problem of nonlinear elastic wave equations of three dimensional isotropic, homogeneous and hyperelastic materials satisfying the null condition, global existence of classical solutions with small initial data was proved in…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
In Class. Quantum Grav. 26 (2009) 175006 (arXiv:0812.4333v3) Bizon et al discuss the power-law tail in the long-time evolution of a spherically symmetric self-gravitating massless scalar field in odd spatial dimensions. They derive explicit…
In this paper, we investigate the fully nonlinear wave equations on the product space $\mathbb{R}^3\times\mathbb{T}$ with quadratic nonlinearities and on $\mathbb{R}^2\times\mathbb{T}$ with cubic nonlinearities, respectively. It is shown…
Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In…
We prove the existence of weak solutions for the one obstacle problem associated with a class of quasilinear wave equations in one space dimension, extending previous results obtained in the linear case, and we also address the two…
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.…
This paper is devoted to the study of asymptotic behaviors of solutions to the one-dimensional defocusing semilinear wave equation. We prove that finite energy solution tends to zero in the pointwise sense, hence improving the averaged…
In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of…
We prove the existence of strong and weak solutions to the semilinear wave equation with coefficients depending both on time and space variables, with continuous nonlinearity satisfying the sign condition. The uniqueness is proven under…
We analyze systems of semilinear wave equations in $3+1$ dimensions whose associated asymptotic equation admit bounded solutions for suitably small choices of initial data. Under this special case of the weak null condition, which we refer…
We numerically evolve spherically symmetric solutions to the linear wave equation on some expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes and study the respective asymptotics for large times. We find a quantitative…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
We study solutions to the linear wave equation on the cosmological region of Schwarzschild-de Sitter spacetimes. We show that all sufficiently regular finite-energy solutions to the linear equation possess a particular finite-order…
Large-time asymptotic properties of solutions to a class of semilinear stochastic wave equations with damping in a bounded domain are considered. First an energy inequality and the exponential bound for a linear stochastic equation are…
We consider a class of quasilinear wave equations in $3+1$ space-time dimensions that satisfy the "weak null condition" as defined by Lindblad and Rodnianski \cite{LR1}, and study the large time behavior of solutions to the Cauchy problem.…
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…