Related papers: On the wave equation with variable exponent nonlin…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
We prove wave breaking --- bounded solutions with unbounded derivatives --- in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope…
This paper deals with a class of semilinear wave equation with nonlinear damping term $|u_{t}|^{m-2}u_t $ and nonlinear source term $g(x)|u|^{p-2}u$ on the manifolds with conical singularities. Firstly, we prove the local existence and…
In this work, we consider a system of multidimensional wave equations coupled by velocities with one localized fractional boundary damping. First, using a general criteria of Arendt- Batty, by assuming that the boundary control region…
In this article, we study the local existence of solutions for a wave equation with a nonlocal in time nonlinearity. Moreover, a blow-up results are proved under some conditions on the dimensional space, the initial data and the nonlinear…
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 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…
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…
This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory…
In this paper, we consider the long time behavior for the solution of a class of variable coefficient wave equation with nonlinear damping and logarithmic source. The existence and uniqueness of local weak solution can be obtained by using…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
For one spatial variable, a new kind of nonlinear wave equation for Emden-Fowler type is considered with boundary value null and initial values. Under certain conditions on the initial data and the exponent p, we exhibit that the…
In this paper, we consider the asymptotic behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We prove that when the damping is effective, the solution is approximated by that of the corresponding…
This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…
In this paper we use a modified test function method to derive nonexistence results for the semilinear wave equation with time-dependent speed and damping. The obtained critical exponent is the same exponent of some recent results on global…
In this paper, we consider a wave equation with strong damping and logarithmic nonlinearity. This paper aims to study the local and global existence, uniqueness and the uniform energy decay rate of a weak solution under some sufficient…
The aim of this paper is to prove a blow up result of the solution for a semilinear scale invariant damped wave equation under a suitable decay condition on radial initial data. The admissible range for the power of the nonlinear term…
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.…