Related papers: Kirchhoff equations with strong damping
We consider the Kirchhoff equation $$ \partial_{tt} u - \Delta u \Big( 1 + \int_{\mathbb T^d} |\nabla u|^2 \Big) = 0 $$ on the $d$-dimensional torus $\mathbb T^d$, and its Cauchy problem with initial data $u(0,x)$, $\partial_t u(0,x)$ of…
A class of energy-transport equations without electric field under mixed Dirichlet-Neumann boundary conditions is analyzed. The system of degenerate and strongly coupled parabolic equations for the particle density and temperature arises in…
In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in [M. D'Abbicco, A wave equation with structural damping and…
In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…
Consider a nonlinear Kirchhoff type equation as follows \begin{equation*} \left\{ \begin{array}{ll} -\left( a\int_{\mathbb{R}^{N}}|\nabla u|^{2}dx+b\right) \Delta u+u=f(x)\left\vert u\right\vert ^{p-2}u & \text{ in }\mathbb{R}^{N}, \\ u\in…
We consider Kirchhoff equations for vibrating bodies in any dimension in presence of a time-periodic external forcing with period 2pi/omega and amplitude epsilon, both for Dirichlet and for space-periodic boundary conditions. We prove…
For general nonlinear Klein-Gordon equations with dissipation we show that any finite energy radial solution either blows up in finite time or asymptotically approaches a stationary solution in $H^1\times L^2$. In particular, any global…
We demonstrate the global existence of weak solutions to a class of semilinear strongly damped wave equations possessing nonlinear hyperbolic dynamic boundary conditions. Our work assumes $(-\Delta_W)^\theta \partial_tu$ with…
We study the Euler equations with the so-called Ekman damping in the whole 2D space. The global well-posedness and dissipativity for the weak infinite energy solutions of this problem in the uniformly local spaces is verified based on the…
In this paper, using the theory developed in [8], we obtain some results of a totally new type about a class of non-local problems. Here is a sample: Let $\Omega\subset {\bf R}^n$ be a smooth bounded domain, with $n\geq 4$, let $a, b,…
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…
In this paper, we consider the 1D compressible Euler equation with the damping coefficient $\lambda/(1+t)^{\mu}$. Under the assumption that $0\leq \mu <1$ and $\lambda >0$ or $\mu=1$ and $\lambda > 2$, we prove that solutions exist globally…
In this paper we consider the local and global well-posedness to the density-dependent incompressible viscoelastic fluids. We first study some linear models associated to the incompressible viscoelastic system. Then we approximate the…
In this paper we consider a porous-elastic system consisting of nonlinear boundary/interior damping and nonlinear boundary/interior sources. Our interest lies in the theoretical understanding of the existence, finite time blow-up of…
This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in…
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have…
We consider the Cauchy problem of the semilinear wave equation with a damping term \begin{align*} u_{tt} - \Delta u + c(t,x) u_t = |u|^p, \quad (t,x)\in (0,\infty)\times \mathbb{R}^N,\quad u(0,x) = \varepsilon u_0(x), \ u_t(0,x) =…
We prove the global-in-time existence of weak solutions to the Navier-Stokes equations of compressible isentropic flow in three space dimensions with adiabatic exponent $\gamma\ge1$. Initial data and solutions are small in $L^2$ around a…
In this paper, we shall investigate the existence and upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with a strong damping in the time-dependent space $X_t$. After deriving the existence and…
We study the Cauchy problem for the semi-linear damped wave equation in any space dimension. We assume that the time-dependent damping term is effective. We prove the global existence of small energy data solutions in the supercritical…