Related papers: Circularization in the damped Kepler problem
The modification of the magnetization dissipation or Gilbert damping caused by an inhomogeneous magnetic structure and expressed in terms of a wave vector dependent tensor $\underline{\alpha}(\vec{q})$ is investigated by means of linear…
The aim of this paper is to give global nonexistence and blow--up results for the problem $$ \begin{cases} u_{tt}-\Delta u+P(x,u_t)=f(x,u) \qquad &\text{in $(0,\infty)\times\Omega$,}\\ u=0 &\text{on $(0,\infty)\times \Gamma_0$,}\\…
Under fairly general assumptions, we prove that every compact invariant subset $\mathcal I$ of the semiflow generated by the semilinear damped wave equation \epsilon u_{tt}+u_t+\beta(x)u-\sum_{ij}(a_{ij} (x)u_{x_j})_{x_i}&=f(x,u),&&…
The asymptotically flat, electrically charged, rotating black holes (BHs) in Einstein-Maxwell-dilaton (EMd) theory are known in closed form for \textit{only} two particular values of the dilaton coupling constant $\gamma$: the…
We consider the semilinear diffusion equation $\partial$ t u = Au + |u| $\alpha$ u in the half-space R N + := R N --1 x (0, +$\infty$), where A is a linear diffusion operator, which may be the classical Laplace operator, or a fractional…
The aim of this paper is to analyze the long-time dynamical behavior of the solution for a degenerate wave equation with time-dependent damping term $\partial_{tt}u + \beta(t)\partial_tu = \mathcal{L}u(x,t) + f(u)$ on a bounded domain…
We construct and analyze a generalization of the Kepler problem. These generalized Kepler problems are parameterized by a triple $(D, \kappa, \mu)$ where the dimension $D\ge 3$ is an integer, the curvature $\kappa$ is a real number, the…
In this paper, we give a geometric approach to the cubic oscillator with three distinct turning points based on the $\mathcal{D\diagup SG}$\emph{\ correspondence }introduced in \cite{Thabet+al}. The existence of quantization conditions,…
Compact objects evolving in an astrophysical environment experience a gravitational drag force known as dynamical friction. We present a multipole-frequency decomposition to evaluate the orbit-averaged energy and angular momentum…
We present a general framework for understanding and analyzing critical behaviour in gravitational collapse. We adopt the method of renormalization group, which has the following advantages. (1) It provides a natural explanation for various…
Damping of magnetization dynamics in a ferromagnetic metal is usually characterized by the Gilbert parameter alpha. Recent calculations of this quantity, using a formula due to Kambersky, find that it is infinite for a perfect crystal owing…
The purpose of this paper is to study the solutions of $$ \Delta u +K(x) e^{2u}=0 \quad{\rm in}\;\; \mathbb{R}^2 $$ with $K\le 0$. We introduce the following quantity: $$\alpha_p(K)=\sup\left\{\alpha \in \mathbb{R}:\, \int_{\mathbb{R}^2}…
The existence of positive solutions is considered for the Dirichlet problem \[ \left\{ \begin{array} [c]{rcll}% -\Delta_{p}u & = & \lambda\omega_{1}(x)\left\vert u\right\vert ^{q-2}% u+\beta\omega_{2}(x)\left\vert u\right\vert…
We study traveling fronts in a system of one dimensional reaction-diffusion-advection equations motivated by problems in reactive flows. In the limit as a parameter tends to infinity, we construct the approximate front profile and determine…
We consider the supercritical problem \[ -\Delta v=|v|^{p-2}v in \Theta_{\epsilon}, v=0 on \partial\Theta_{\epsilon}, \] where $\Theta$ is a bounded smooth domain in $\mathbb{R}^{N}$, $N\geq3$, $p>2^{\ast}:=2N/(N-2)$, and…
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…
We phenomenologically derive a cosmological model that includes both a cosmological constant term $\Lambda/3$ and a dissipative driving term $\beta (2 H^{2} + \dot{H})$ by applying both the first law of thermodynamics and an effective…
In this paper we perform a refined blow up analysis of finite energy approximated solutions to a Nirenberg type problem on half spheres. The later consists of prescribing, under minimal boundary conditions, the scalar curvature to be a…
This paper studies the existence of positive normalized solutions to the singular elliptic equation \[ -\Delta u + \lambda u = u^{-r} + u^{p-1} \quad \text{in } \Omega, \] with the Dirichlet boundary condition $u=0$ on $\partial\Omega$ and…
The purpose of this paper is to give a characterization of the structure of non-autonomous attractors of the problem $u_t= u_{xx} + \lambda u - \beta(t)u^3$ when the parameter $\lambda > 0$ varies. Also, we answer a question proposed in…