相关论文: A note on time-asymptotic bounds with a sharp alge…

In this paper, we study the time-space fractional differential equation of the Volterra type: \begin{align*} {D}^\alpha_{0 \vert t} (u) +(-\Delta_N)^{\sigma}u &= u(1+au-bu^2)-au\int_0^t {K}(t-s) u(\cdot) \, ds, \end{align*} where $a,b>0$…

We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic…

This paper is concerned with the existence/nonexistence of nontrivial global-in-time solutions to the Cauchy problem \begin{equation} \begin{cases}\tag{P}\partial_tu-\partial_x^2u+Vu=(1+x^2)^{-\frac{m}{2}}u^p,&x\in\mathbb{R},\ t>0,\\…

Consider the equation u_t=\Delta u-Vu +au^p \text{in} R^n\times (0,T); u(x,0)=\phi(x)\gneq0, \text{in} R^n, where $p>1$, $n\ge2$, $T\in(0,\infty]$, $V(x)\sim\frac\omega{|x|^2}$ as $|x|\to\infty$, for some $\omega\neq0$, and $a(x)$ is on the…

We apply periodic orbit theory to study the asymptotic distribution of escape times from an intermittent map. The dynamical zeta function exhibits a branch point which is associated with an asymptotic power law escape. By an analytic…

We give an explicit representation of the fundamental solution to the heat equation on a half-space of ${\mathbb R}^N$ with the homogeneous dynamical boundary condition, and obtain upper and lower estimates of the fundamental solution.…

Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…

In the analysis of highly-oscillatory evolution problems, it is commonly assumed that a single frequency is present and that it is either constant or, at least, bounded from below by a strictly positive constant uniformly in time. Allowing…

This paper is devoted to the asymptotic behavior of global solutions to the convection-diffusion equation in the Fujita-subcritical case. We improve the result by Zuazua (1993) and establish higher order asymptotic expansions with decay…

This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…

A sufficient condition for asymptotic stability of the zero solution to an abstract nonlinear evolution problem is given. The governing equation is $\dot{u}=A(t)u+F(t,u),$ where $A(t)$ is a bounded linear operator in Hilbert space $H$ and…

We consider a nonlinear Fokker-Planck equation derived from a Cucker-Smale model for flocking with noise. There is a known phase transition depending on the noise between a regime with a unique stationary solution which is isotropic…

We prove some sharp regularity results for solutions of classical first order hyperbolic initial boundary value problems. Our two main improvements on the existing litterature are weaker regularity assumptions for the boundary data and…

A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the…

We study semilinear third-order (in time) evolution equations with fractional Laplacian $(-\Delta)^{\sigma}$ and power nonlinearity $|u|^p$, which was proposed by Bezerra-Carvalho-Santos [2] recently. In this manuscript, we obtain a new…

We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…

This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…

Strong anomalous diffusion is {often} characterized by a piecewise-linear spectrum of the moments of displacement. The spectrum is characterized by slopes $\xi$ and $\zeta$ for small and large moments, respectively, and by the critical…

We consider semilinear higher order (in time) evolution inequalities posed in an exterior domain of the half-space $\mathbb{R}_+^N$, $N\geq 2$, and involving differential operators of the form $\mathcal{L}_\lambda =-\Delta +\lambda/|x|^2$,…

We consider the equation $-\Delta u= |x|^{\alpha}|u|^{p-1}u$ for any $\alpha\geq 0$, either in $\mathbb R^2$ or in the unit ball $B$ of $\mathbb R^2$ centered at the origin with Dirichlet or Neumann boundary conditions. We give a sharp…