共查询到10条相似文献,搜索用时 876 毫秒
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Zhang Lixun Liu Yongzhi Wang Kangning 《高校应用数学学报(英文版)》2006,21(1):41-44
The construction of solution for three-order evolution equation xttt=A^3x is skillfully obtained and the semigroup of equation operator is theoretically proved,then the solution for three-order evolution equation xttt+iCx=f is constructed from the appropriate transformation, and the necessary and sufficient conditions of its unitary semigroup are presented. 相似文献
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《Applied Mathematics Letters》2006,19(2):206-214
In this work, we study the differentiability of the stationary age-dependent population system based on parity progression. By using the semigroup approach, we prove that the solution semigroup of the population evolution equation is eventually differentiable. 相似文献
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本文在[3],[4]工作的基础上,利用变数算符的思想以及Mikusinski算符域中移动算符和变系数移动算符级数的有关结果,解决了一般的三阶线性变系数差分方程的求解问题,并且绘出了一些特殊的三阶线性变系数差分方程的更好的解式;此外,还试图为实现更高阶线性变系数差分方程的求解提供思想方法。 相似文献
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根据非游荡算子半群的定义得到了非游荡算子半群的几个性质,给出了判定算子半群是非游荡半群的标准,应用给出的标准,在空间C([0,1],C)上讨论了偏微分方程au/at=γx(au/ax)+h(x)u,u(0,x)=f(x)的解半群的性质. 相似文献
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This paper investigates the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. Based on the operator semigroup theory, we transform the time-space fractional reaction-diffusion equation into an abstract evolution equation. The existence and uniqueness of mild solution to the reaction-diffusion equation are obtained by solving the abstract evolution equation. Finally, we verify the Mittag-Leffler-Ulam stabilities of the nonlinear time-space fractional reaction-diffusion equations with nonlocal initial conditions. The results in this paper improve and extend some related conclusions to this topic. 相似文献
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This paper is concerned with asymptotic stability of Mindlin–Timoshenko plates with dissipation of Kelvin–Voigt type on the equations for the rotation angles. We prove that the corresponding evolution semigroup is analytic if a viscoelastic damping is also effective over the equation for the transversal displacements. On the contrary, if the transversal displacement is undamped, we show that the semigroup is neither analytic nor exponentially stable. In addition, in the latter case, we show that the solution decays polynomially and we prove that the decay rate found is optimal. 相似文献
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Ulrich Hornung 《manuscripta mathematica》1982,39(2-3):155-172
An existence and uniqueness result is proved for a variational inequality of evolution. The problem consists of a nonlinear parabolic/elliptic differential equation for which Dirichlet, Neuman and Signorini boundary conditions are posed. The existence is obtained using a regularization process, while uniqueness is based on L1-contractiveness of the solution semigroup. 相似文献
10.
Stefano Bonaccorsi Gertrud Desch 《NoDEA : Nonlinear Differential Equations and Applications》2013,20(3):557-594
We consider a class of infinite delay equations in Banach spaces that models arising in the theory of viscoelasticity, for instance. The equation involves a completely monotone convolution kernel with a singularity at t = 0 and a sectorial linear spatial operator. Our main goal here is the construction of a semigroup formulation for the integral equation; in the last part of the paper, we illustrate the potentiality of the approach by considering a stochastic perturbation of the problem. Existence and uniqueness of a weak solution is established. The corresponding evolutionary solution process is Markovian, and the tools of linear analytic semigroup theory can be utilized. 相似文献