Related papers: Stochastic Wave Equations with Nonlinear Damping a…
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…
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 paper, we consider the wave equation with variable coefficients and boundary damping and supercritical source terms. The goal of this work is devoted to prove the local and global existence, and classify decay rate of energy…
The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data are posed in the energy space. The aim of the paper is to…
In this paper, we consider the initial boundary value problem in an exterior domain for semilinear strongly damped wave equations with power nonlinear term of the derivative-type $|u_t|^q$ or the mixed-type $|u|^p+|u_t|^q$, where $p,q>1$.…
This paper deals with the following Petrovsky equation with damping and nonlinear source \[u_{tt}+\Delta^2 u-M(\|\nabla u\|_2^2)\Delta u-\Delta u_t+|u_t|^{m(x)-2}u_t=|u|^{p(x)-2}u\] under initial-boundary value conditions, where $M(s)=a+…
This paper is devoted to studying the following two initial-boundary value problems for semilinear wave equations with variable coefficients on exterior domain with subcritical exponent in $n$ space dimensions:…
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…
In this paper, we investigate the initial boundary value problem of the following nonlinear extensible beam equation with nonlinear damping term $$u_{t t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta u_t+\left|u_t\right|^{r-1}…
We consider the initial boundary value problem in exterior domain for strongly damped wave equations with power type nonlinearity |u|^p. We will establish blow-up results under some conditions on the initial data and the exponent p.
We explore the relation between fast waves, damping and imposed noise for different scalings by considering the singularly perturbed stochastic nonlinear wave equations \nu u_{tt}+u_t=\D u+f(u)+\nu^\alpha\dot{W} on a bounded spatial domain.…
This article focuses on a quasilinear wave equation of $p$-Laplacian type: $$ u_{tt} - \Delta_p u - \Delta u_t=0$$ in a bounded domain $\Omega\subset\mathbb{R}^3$ with a sufficiently smooth boundary $\Gamma=\partial\Omega$ subject to a…
The paper is concerned with the problem of explosive solutions for a class of nonlinear stochastic wave equations in a domain $\mathcal{D}\subset\mathbb{R}^d$ for $d\leq3$. Under appropriate conditions on the initial data, the nonlinear…
We consider the initial boundary value problem in exterior domain for semilinear wave equations with power-type nonlinearity |u| p. We will establish blow-up results when p is less than or equal to Strauss' exponent which is the same one…
We consider a class of wave equations with constant damping and polynomial nonlinearities that are perturbed by small, multiplicative, space-time white noise. The equations are defined on a one-dimensional bounded interval with Dirichlet…
In this paper we show existence of finite energy solutions for the Cauchy problem associated with a semilinear wave equation with interior damping and supercritical source terms. The main contribution consists in dealing with…
We consider the defocusing nonlinear wave equation $u_{tt}-\Delta u + |u|^p u=0$ in the energy-supercritical regime p>4. For even values of the power p, we show that blowup (or failure to scatter) must be accompanied by blowup of the…
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…
In this paper, we consider the semilinear damped wave equation with nonlinearities of derivative type $|u_t|^p$. We observe that this problem admits a unique global (in time) solution with small initial data for all $p > 1$ in low spatial…
In this paper we consider the nonlinear dispersive wave equation on the real line, $u_t-u_{txx}+[f(u)]_x-[f(u)]_{xxx}+\bigl[g(u)+\frac{f''(u)}{2}u_x^2\bigr]_x=0$, that for appropriate choices of the functions $f$ and $g$ includes well known…