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11.
We establish the existence and stability of multidimensional transonic shocks for the Euler equations for steady potential compressible fluids. The Euler equations, consisting of the conservation law of mass and the Bernoulli law for the velocity, can be written as a second-order, nonlinear equation of mixed elliptic-hyperbolic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the location of the transonic shock which divides the two regions of smooth flow, and the equation is hyperbolic in the upstream region where the smooth perturbed flow is supersonic. We develop a nonlinear approach to deal with such a free boundary problem in order to solve the transonic shock problem. Our results indicate that there exists a unique solution of the free boundary problem such that the equation is always elliptic in the downstream region and the free boundary is smooth, provided that the hyperbolic phase is close to a uniform flow. We prove that the free boundary is stable under the steady perturbation of the hyperbolic phase. We also establish the existence and stability of multidimensional transonic shocks near spherical or circular transonic shocks.
12.
We consider a useful modification of the inexact implicit method with a variable parameter in Wang et al. J Optim Theory 111:
431–443 (2001) for generalized mixed monotone variational inequalities. One of the contributions of the proposed method in
this paper is that the restrictions imposed on the variable parameter are weaker than the ones in Wang et al. J Optim Theory
111: 431–443 (2001). Another contribution is that we establish a sufficient and necessary condition for the convergence of
the proposed method to a solution of the general mixed monotone variational inequality. 相似文献
13.
M. Akbari A. Behzadmehr F. Shahraki 《International Journal of Heat and Fluid Flow》2008,29(2):545-556
Fully developed laminar mixed convection of a nanofluid consists of water and Al2O3 in horizontal and inclined tubes has been studied numerically. Three-dimensional elliptic governing equations have been solved to investigate the flow behaviors over a wide range of the Grashof and Reynolds numbers. Comparisons with previously published experimental and numerical works on mixed convection in a horizontal and inclined tube are performed and good agreements between the results are observed. Effects of nanoparticles concentration and tube inclinations on the hydrodynamics and thermal parameters are presented and discussed. It is shown that the nanoparticles concentration does not have significant effects on the hydrodynamics parameters. Heat transfer coefficient increases by 15% at 4 Vol.% Al2O3. Skin friction coefficient continually increases with the tube inclination, but the heat transfer coefficient reaches a maximum at the inclination angle of 45°. 相似文献
14.
研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果. 相似文献
15.
16.
本文用变换群理论对运动水平平板混合对流边界层流动的动量、能量和浓度扩散方程进行了分析,得到了与X4/(7-5n)成正比的壁面温度分布和浓度分布,同时壁面运动速度正比于X(3-n)/(7-5n)时存在相似性解.导出了相似性解方程,用四阶Runge-Kutta方法进行了计算,给出了Pr=0.72 和Sc,K1,K2,K3参数下的速度、温度和浓度分布,得出了各参数对流场、温度场的影响。 相似文献
17.
Tatsien Li 《Mathematical Methods in the Applied Sciences》2006,29(13):1543-1553
By means of a direct and constructive method based on the theory of semi‐global C2 solution, the local exact boundary observability and an implicit duality between the exact boundary controllability and the exact boundary observability are shown for 1‐D quasilinear wave equations with various boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
18.
Gabriel N. Gatica Ernst P. Stephan 《Numerical Methods for Partial Differential Equations》2002,18(1):105-128
This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002 相似文献
19.
This work is aimed at the optimization of the yield and purity of non-symmetrical trialkyl sulfonium halide salts. The effects of parameters such as solvent, temperature and concentration were studied. The products were carefully analyzed and the crystal structure of [{n-CH3(CH2)15}(CH3)2S]Br determined. The overall aim of the present study is future syntheses of low-dimensional magnetic materials. 相似文献
20.