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31.
研究一类脉冲时滞抛物型偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在两类不同边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用. 相似文献
32.
A. V. Martynenko A. F. Tedeev 《Computational Mathematics and Mathematical Physics》2007,47(2):238-248
The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered: . The conditions on the parameters of the problem are found under which the solution to the Cauchy problem blows up in a finite time. A sharp universal (i.e., independent of the initial function) estimate of the solution near the blowup time is obtained.
相似文献
$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + u^p $
33.
半线性抛物型方程组解的整体存在性与爆破速率估计 总被引:1,自引:0,他引:1
研究了具有非线性热源的半线性抛物型方程组的齐次neumann问题解的爆破性质.利用上下解方法得到了解整体存在的条件与爆破条件,并利用FriedmannMcleod方法建立了爆破速率估计. 相似文献
34.
Li Chen Ling Hsiao Gerald Warnecke 《应用数学学报(英文版)》2007,23(1):9-28
This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity. 相似文献
35.
In this paper, we discuss the controllability of a nonlinear degenerate parabolic system with bilinear control. Based on the shrinking property of the solutions, we prove that the system is not globally approximately controllable. Furthermore, we give an approximate null controllability result. We also prove that the system is not globally exactly null controllable by a comparison principle. 相似文献
36.
37.
In this note new Rosenbrock methods for ODEs, DAEs, PDEs and PDAEs of index 1 are presented. These solvers are of order 3,
have 3 or 4 internal stages, and fulfil certain order conditions to obtain a better convergence if inexact Jacobians and approximations
of
are used. A comparison with other Rosenbrock solvers shows the advantages of the new methods.
AMS subject classification (2000) 34A09, 65L80 相似文献
38.
Chiara Manzini 《Physica D: Nonlinear Phenomena》2010,239(15):1402-1415
The asymptotic analysis of a linear high-field Wigner-BGK equation is developed by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number ?, evolution equations are derived for the terms of zeroth and first order in ?. In particular, a quantum drift-diffusion equation for the position density of electrons, with an ?-order correction on the field terms, is obtained. Well-posedness and regularity of the approximate problems are established, and a rigorous proof that the difference between exact and asymptotic solutions is of order ?2, uniformly in time and for arbitrary initial data is given. 相似文献
39.
考 虑具有未 知源项的 某些非 线性伪 抛物 型方程 的反演 问题. 首先 将伪抛 物型 方程初 边值问 题化为非线 性发展方 程 Couch y 问题,然 后,利用半 群理论,论 证发展 方程反问 题解的存 在唯一 性,最后, 利用不 动点方法得到 伪抛物型方程反 问题的可解性 相似文献
40.
We consider systems of partial differential equations, which contain only second derivatives in the x variables and which are uniformly parabolic in the sense of Petrovskii. For such systems we obtain necessary and, separately, sufficient conditions for the maximum norm principle to hold in the layer Rn × ( 0,T ] and in the cylinder × ( 0,T], where is a bounded subdomain of Rn. In this paper the norm is understood in a generalized sense, i.e. as the Minkowski functional of a compact convex body in Rm containing the origin. The necessary and sufficient conditions coincide if the coefficients of the system do not depend on t. The criteria for validity of the maximum norm principle are formulated as a number of equivalent algebraic conditions describing the relation between the geometry of the unit sphere of the given norm and coefficients of the system under consideration. Simpler formulated criteria are given for certain classes of norms: for differentiable norms, p-norms ( 1 p ) in Rm, as well as for norms whose unit balls are m-pyramids, m-bipyramids, cylindrical bodies, m-parallelepipeds. The case m = 2 is studied separately. 相似文献