相关论文: Decay rates for the 4D energy-critical nonlinear h…

In this article, we study a semi-linear heat equation with the nonlinearity which is the product of polynomial and logarithmic functions. Using the invariance of the potential well(s), we have established the global existence and…

An algebraic upper bound for the decay rate of solutions to the Navier-Stokes and Navier-Stokes-Coriolis equations in the critical space $\dot{H} ^{\frac{1}{2}} (\mathbb{R} ^3)$ is derived using the Fourier Splitting Method. Estimates are…

We examine the energy-critical nonlinear heat equation in critical spaces for any dimension greater or equal than three. The aim of this paper is two-fold. First, we establish a necessary and sufficient condition on initial data at or below…

We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension $d \geq 5$. By employing the Fourier splitting method, we establish precise decay rates for…

We address the study of decay rates of solutions to dissipative equations. The characterization of these rates is given for a wide class of linear systems by the {\em decay character}, which is a number associated to the initial datum that…

We study solutions of the focusing energy-critical nonlinear heat equation $u_t = \Delta u - |u|^2u$ in $\mathbb{R}^4.$ We show that solutions emanating from initial data with energy and $\dot{H}^1-$norm below those of the stationary…

We consider the six dimensional energy-critical semilinear heat equation with self-similarly decaying initial data. Our main result shows the existence of sign-changing solutions that exhibit infinite-time blow-up and nonnegative solutions…

Global classical solutions to the viscous Hamilton-Jacobi equation with homogenious Dirichlet boundary conditions are shown to converge to zero at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to…

We study the Cauchy problem for a nonlocal heat equation, which is of fractional order both in space and time. We prove four main theorems: (i) a representation formula for classical solutions, (ii) a quantitative decay rate at which the…

In this paper, we study the energy decay for the thermoelastic Bresse system in the whole line with two different dissipative mechanism, given by heat conduction (Types I and III). We prove that the decay rate of the solutions are very…

We are concerned with the time decay rates of strong solutions to a non-conservative compressible viscous two-phase fluid model in the whole space R3. Compared to the previous related works, the main novelty of this paper lies in the fact…

We prove optimal estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations in $\mathbb{R}^d$. An important special case is the time-fractional diffusion equation, which has seen much…

In this paper we establish optimal pointwise decay estimates for non-dispersive (compact) radial solutions to non-linear wave equations in 3 dimensions, in the energy supercritical range. As an application, we show for the full energy…

Infinite energy solutions to the Navier-Stokes equations in $\mathbb{R}^2$ may be constructed by decomposing the initial data into a finite energy piece and an infinite energy piece, which are then treated separately. We prove that the…

We prove pointwise-in-time dispersive decay for solutions to the energy-critical nonlinear Schr\"odinger equation in spatial dimensions $d = 3,4$ for both the initial-value and final-state problems.

In this paper we obtain bounds for the decay rate for solutions to the nonlocal problem $\partial_t u(t,x) = \int_{\R^n} J(x,y)[u(t,y) - u(t,x)] dy$. Here we deal with bounded kernels $J$ but with polynomial tails, that is, we assume a…

We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as…

In this note, we prove pointwise decay in time of solutions to the 3D energy-critical nonlinear Schr\"odinger equations assuming data in $L^1\cap H^3$. The main ingredients are the boundness of the Schr\"odinger propagators in Hardy space…

We prove the decay in the energy space for the solution to the defocusing biharmonic Hartree-Fock equations with mass-supercritical and energy-subcritical Choquard-type nonlinearity in space dimension $d\geq3$. We treat both the free and…

In this paper, hypocoercivity methods are applied to linear kinetic equations with mass conservation and without confinement, in order to prove that the solutions have an algebraic decay rate in the long-time range, which the same as the…