Related papers: Critical exponent for nonlinear wave equations wit…

We study in this article the blow-up of solutions to a coupled semilinear wave equations which are characterized by linear damping terms in the \textit{scale-invariant regime}, time-derivative nonlinearities, mass terms and Tricomi terms.…

Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…

The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then…

This paper studies the large-time behavior of solutions to the quasilinear inhomogeneous parabolic equation with combined nonlinearities. This equation is a natural extension of the heat equations with combined nonlinearities considered by…

This paper studies the upper and lower bounds of the lifespan for the classical solutions to the initial value problems of one dimensional wave equations with non-autonomous semilinear terms including the space-derivative of the unknown…

In this paper we prove the blow-up theorem in the critical case for weakly coupled systems of semilinear wave equations in high dimensions. The upper bound of the lifespan of the solution is precisely clarified.

In this work, we consider the energy-supercritical defocusing cubic nonlinear wave equation in dimension d=5 for radially symmetric initial data. We prove that an a priori bound in the critical space implies global well-posedness and…

An improvement of [18] on the blow-up region and the lifespan estimate of a weakly coupled system of wave equations with damping and mass in the scale-invariant case and with time-derivative nonlinearity is obtained in this article. Indeed,…

We investigate the problem of entire solutions for a class of fourth order, dilation invariant, semilinear elliptic equations with power-type weights and with subcritical or critical growth in the nonlinear term. These equations define non…

We consider a second order linear equation with a time-dependent coefficient c(t) in front of the "elastic" operator. For these equations it is well-known that a higher space-regularity of initial data compensates a lower time-regularity of…

We consider the $L^2$-critical nonlinear Schrodinger equation with an inhomogeneous damping term. We prove that there exists an initial data such that the corresponding solution is global in $H^1(R^d)$ and we give the minimal time of the…

This article presents a new scheme for studying the dynamics of a quintic wave equation with nonlocal weak damping in a 3D smooth bounded domain. As an application, the existence and structure of weak, strong, and exponential attractors for…

The topic of this paper is a semi-linear, defocusing wave equation $u_{t t}-\Delta u=-|u|^{p-1} u$ in sub-conformal case in the higher dimensional space whose initial data are radical and come with a finite energy. We prove some decay…

It is shown that a one-dimensional damped wave equation with an odd time derivative nonlinearity exhibits small amplitude bifurcating time periodic solutions, when the bifurcation parameter is the linear damping coefficient is positive and…

In this short notice, we prove the non-existence of global solutions to the semilinear damped wave equation on the half-space, and we determine the critical exponent for any space dimension.

The main purpose of this expository note is to give a short account of the recent developments in mathematical wave kinetic theory. After reviewing the physical theory, we explain the importance of the notion of a scaling law, which…

We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based…

This paper is concerned with weighted energy estimates for solutions to wave equation $\partial_t^2u-\Delta u + a(x)\partial_tu=0$ with space-dependent damping term $a(x)=|x|^{-\alpha}$ $(\alpha\in [0,1))$ in an exterior domain $\Omega$…

We consider a nonlinear Dirichlet problem driven by a variable exponent $p$-Laplacian plus an indefinite potential term. The reaction has the competing effects of a parametric concave (sublinear) term and of a convex (superlinear)…

We consider a strongly damped semilinear wave equation with initial data prescribed as $(\varrho\phi,\varrho h)$, where the profiles are fixed and only the amplitude $\varrho>0$ is allowed to vary. The question addressed here is how this…