具粘性拟线性波方程的能量衰减估计

给出下列具粘性拟线性波方程初边值问题解的能量衰减估计u_(tt)(t,x)-div{σ(|▽u(t,x)|~2)▽u(t,x)}-△u(t,x)-△ut(t,x)+δ|u_t(t,x)|~(p-1)u_t(t,x)=μ|u(t,x)|~(q-1)u(t,x),x∈Ω,t∈(0,T),u(t,x)|■Ω=0,t∈(0,T),u(0,x)=u_0(x),u_t(0,x)=u_1(x),x∈Ω,其中Ω是R~N(N≥1)中具有光滑边界■Ω的区域,p≥1,q1,δ0,μ0,△表示Laplace算子,▽表示梯度算子和σ(s)是一给定的非线性函数.证明的思想是应用一已知的积分不等式,证明以上初边值问题解的能量衰减估计.     

带地形作用的正压方程组的Cauchy问题适定性(Ⅱ):粘性

带地形作用的粘性正压方程组不是Cauchy-Kowalewska型,但利用分层理论可证明它是稳定的,并且给出解空间的分层结构以及Cauchy问题适定性的判别标准．证明了在超平面{t=t^0}包含R^2上粘性正压方程组是不适定的。     

偶数维空间带粘性项的非线性波动方程解的衰减估计

基于对线性化方程格林函数的详细分析,研究了偶数维空间带粘性项的非线性波动方程解的大时间状态.得到了解的最佳衰减估计,与惠更斯原理相符.     

一类具有粘性项的拟线性抛物型方程组*

研究了一类具有非线性源项和粘性项的拟线性抛物型方程组的初边值问题．通过构造稳定集, 证明了此问题整体解的存在性, 并建立了解的长时间行为．同时在放松函数的适当假设条件下, 得到了初始能量非负时解的爆破性质及解的生命区间估计．     

一类退化非线性抛物型方程整体解的衰减估计

J.L.L ions用紧致性方法证明了一类退化非线性抛物型方程初边值问题整体解的存在唯一性,但解的衰减性很少有人考虑.应用M.N akao建立的差分不等式研究了整体解的衰减估计.     

高频超声中带退化记忆项的MGT方程解的衰减估计北大核心CSCD

研究了高频超声应用中带无穷退化记忆项的Moore-Gibson-Thompson方程τu_(ttt)+α(x)u_(tt)-c^(2)Δu-bΔu_(t)+∫^(∞)_(0)g(s)div[a(x)▽u(t-s)]ds=0解的适定性和衰减速率,其中非负函数a(x)和α(x)是可退化的并满足a(x)+α(x)≥δ>0.该系统是由黏性热松弛流体中波传播模型的线性化而得到的.通过使用Faedo-Galerkin逼近和能量估计,证明了解的适定性.在适当的假设下,通过构造适当的李雅普诺夫泛函,建立了能量的指数或一般衰减结果.     

带有对数非线性源的p-Kirchhoff方程解的整体存在性和衰减估计

考虑带有对数非线性源的p-Kirchhoff方程的初边值问题,此问题可用来描述热传播的过程和种群密度的演化.首先利用Galerkin方法,对数Sobolev不等式以及Gronwall不等式,再结合Lions引理,得到其局部解的存在性.同时引入修正泛函研究势井深度,结合势井理论,建立先验估计,得到解的整体存在性和衰减估计,推广和改进了已有结果.     

Global Well-Posedness of the BCL System with Viscosity

The BCL system, a kind of equations governing the motion of the free surface of water waves in R3, is studied. Some results on the global existence, uniqueness and regularity of solutions to such system with small initial data are obtained.     

三维广义磁流体方程组解的最优衰减率

本文利用Fourier分解法首次建立了三维广义磁流体动力学方程组弱解的时间衰减估计,得到了该方程解关于时间衰减的上下界估计,并且获得了相应的最优代数衰减率.     

Decay Estimates of Solutions to Wave Equations in Conical Sets

We consider the wave equation in an unbounded conical domain, with initial conditions and boundary conditions of Dirichlet or Neumann type. We give a uniform decay estimate of the solution in terms of weighted Sobolev norms of the initial data. The decay rate is the same as in the full space case.     

三维趋化流体耦合系统整体解的最优衰减估计北大核心CSCD

本文主要研究一类由抛物-抛物型Keller-Segel方程组和粘性不可压Navier-Stokes方程组耦合而成的三维非线性耗散系统.利用Bony微局部分析和Besov空间插值理论,作者建立了该系统在临界Besov空间中小初值问题整体解的最优衰减估计,将[Zhao J H,Zhou J J.Temporal decay in negative Besov spaces for the 3D coupled chemotaxis-fluid equations [J].Nonlinear Analysis:Real World Applications,2018,42:160-179.]中的衰减结果的可积性指标推广至了更一般的情形.     

Decay Estimates for Solutions of Porous Medium Equations with Advection

In this paper, we show that bounded weak solutions of the Cauchy problem for general degenerate parabolic equations of the form

$$ u_{t} + \operatorname{div}f(x,t,u) = \operatorname{div}\bigl( |u|^{\alpha } \nabla u\bigr), \quad x \in \mathbb{R}^{n} , \ t > 0, $$

where \(\alpha > 0 \) is constant, decrease to zero, under fairly broad conditions on the advection flux \(f\). Besides that, we derive a time decay rate for these solutions.

     

拟线性方程非局部边值问题解的衰减估计

本文讨论一类源于拟静态热弹性力学和控制理论等领域的边值问题,通过构造适当的上下解得到拟线性方程解的衰减估计。     

Some Estimates near the Boundary for Solutions to the Nonstationary Linearized Navier–Stokes Equations

In the present paper, new local estimates near the boundary are established for solutions to the nonstationary linearized Navier–Stokes equations are established. Bibliography: 8 titles.     

Decay Estimates for Solutions of Linear Elasticity for Anisotropic Media

We analyse the time decay of solutions to the Cauchy problem for the linear hyperbolic system of elasticity for anisotropic media. As an example, we will consider media with hexagonal symmetry. First we derive decay estimates for special initial data using the method of stationary phase in several variables and degenerate phase function based on the Malgrange preparation theorem. Asymptotic expansions are given to prove the sharpness of the weaker time decay found for zinc and beryl than in the isotropic case. A method using Besov spaces leads to ℒ︁^p–ℒ︁^q-estimates.     

Spatial Decay Estimates for the Solutions to Stokes Equations in Four Kinds of Semi-Infinite Cylinders

This paper investigates the spatial behavior of the solutions of the Stokes equations in a semi-infinite cylinder.We consider four kinds of semi-infinite cylind...