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11.
Guowei LIU 《数学物理学报(B辑英文版)》2017,37(1):79-96
This paper studies the time asymptotic behavior of solutions for a nonlinear convection diffusion reaction equation in one dimension.First,the pointwise estimates of solutions are obtained,furthermore,we obtain the optimal L~p,1≤ p ≤ +∞,convergence rate of solutions for small initial data.Then we establish the local existence of solutions,the blow up criterion and the sufficient condition to ensure the nonnegativity of solutions for large initial data.Our approach is based on the detailed analysis of the Green function of the linearized equation and some energy estimates. 相似文献
12.
In this paper, we generalize Bernstein's theorem characterizing the space
by means of local approximations. The closed interval
is partitioned into disjoint half-intervals on which best approximation polynomials of degree
divided by the lengths of these half-intervals taken to the power
are considered. The existence of the limits of these ratios as the lengths of the half-intervals tend to zero is a criterion for the existence of the
th derivative of a function. We prove the theorem in a stronger form and extend it to the spaces
. 相似文献
13.
Henryk Michalewski 《Proceedings of the American Mathematical Society》2003,131(11):3601-3606
For a coanalytic-complete or -complete subspace of a Polish space we prove that there exists a continuous bijection of onto the Hilbert cube . This extends results of Pytkeev. As an application of our main theorem we give an answer to some questions of Arkhangelskii and Christensen.
Under the assumption of Projective Determinacy we also give some generalizations of these results to higher projective classes.
14.
The purpose of this paper is to characterize the pointwise rate of convergence for the combinations of Szász-Mirakjan operators using Ditzian-Totik modulus of smoothness. 相似文献
15.
We consider the space D(X, Y) of densely continuous forms introduced by Hammer and McCoy [5] and investigated also by Holá [6]. We show some additional
properties of D(X, Y) and investigate the subspace D*(X) of locally bounded real-valued densely continuous forms equipped with the topology of pointwise convergence τ-
p
. The largest part of the paper is devoted to the study of various cardinal functions for (D*(X), τ
p
), in particular: character, pseudocharacter, weight, density, cellularity, diagonal degree, π-weight, π-character, netweight etc.
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-006904. The authors would
like to thank Ľubica Holá for suggestions and comments. 相似文献
16.
This paper considers a posteriori error estimates by averaged gradients in second order parabolic problems. Fully discrete
schemes are treated. The theory from the elliptic case as to when such estimates are asymptotically exact, on an element,
is carried over to the error on an element at a given time. The basic principle is that the elliptic theory can be extended
to the parabolic problems provided the time-step error is smaller than the space-discretization error. Numerical illustrations
confirming the theoretical results are given. Our results are not practical in the sense that various constants can not be
estimated realistically. They are conceptual in nature.
AMS subject classification (2000) 65M60, 65M20, 65M15 相似文献
18.
NONLINEAR EVOLUTION SYSTEMS AND GREEN’S FUNCTION 总被引:1,自引:1,他引:0
王维克 《数学物理学报(B辑英文版)》2010,(6):2051-2063
In this paper, we will introduce how to apply Green’s function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen’s principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green’s function of the linearized system and micro-local analysis, such as frequency decomposition and so on. 相似文献
19.
《复变函数与椭圆型方程》2012,57(4):285-301
Let U be the open unit disc of the complex plane. We explicitly construct the best pointwise approximation for determining a function in the Hardy space H p (U) from measured data at a countable set of points in U whenever the data is exact. A regularization scheme is given to deal with the case of nonexact data. Moreover, optimal error estimates are also studied. 相似文献
20.
本文讨论方向数据密度函数核估计的逐点收敛速度问题,在较为温和的条件下建立了该核估计的重对数律并给出了它的逐点最优收敛速度. 相似文献