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111.
Zonglao Zhang 《Journal of Mathematical Analysis and Applications》2005,305(2):491-501
In this paper we investigate the mean curvature H of a radial graph in hyperbolic space Hn+1. We obtain an integral inequality for H, and find that the lower limit of H at infinity is less than or equal to 1 and the upper limit of H at infinity is more than or equal to −1. As a byproduct we get a relation between the n-dimensional volume of a bounded domain in an n-dimensional hyperbolic space and the (n−1)-dimensional volume of its boundary. We also sharpen the main result of a paper by P.-A. Nitsche dealing with the existence and uniqueness of graph-like prescribed mean curvature hypersurfaces in hyperbolic space. 相似文献
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A class of stable least-square finite element methods for non-linear hyperbolic problems is developed and some exploratory studies made. The methods are based on modifying the L2-norm of the. residual and a related approximation to the H1-norm of the residual. The effect of the additional terms in these residual functionals is to introduce a dissipative effect proportional to the solution gradient. This acts to stabilize the solution for non-linear hyperbolic problems which generate shocks. Numerical results for a one-dimensional nozzle and shock tube problem demonstrate the accuracy and stability of the method. Results are for an implicit scheme and calculations for linear, quadratic and cubic elements are given. 相似文献
114.
Takayuki Kobayashi Takayuki Kubo Kenji Nakamura 《Journal of Differential Equations》2018,264(10):6061-6081
In this paper, we discuss a local energy decay estimate of solutions to the initial-boundary value problem for the hyperbolic type Stokes equations of incompressible fluid flow in an exterior domain and a perturbed half-space. The equations are linearized version of the hyperbolic Navier–Stokes equations introduced by Racke and Saal [15], which are obtained as a delayed case for the deformation tensor in the incompressible Navier–Stokes equations. Our proof of the local energy decay estimate is based on Dan and Shibata [2]. In [2], they treated the dissipative wave equations in an exterior domain and discussed the local energy decay estimate. Our approach uses the fact that applying the Helmholtz projection to the hyperbolic type Stokes equations, we obtain equations similar to the dissipative wave ones. 相似文献
115.
Armando V. Corro Francisco Milán 《Journal of Mathematical Analysis and Applications》2010,366(2):582-592
We construct examples of flat surfaces in H3 which are graphs over a two-punctured horosphere and classify complete embedded flat surfaces in H3 with only one end and at most two isolated singularities. 相似文献
116.
Min Yang 《Applied mathematics and computation》2010,215(9):3239-3248
In this paper, we develop a two-time level alternating direction implicit (ADI) method for a class of second-order hyperbolic problems on a rectangular domain. The method builds on the finite volume method with biquadratic basis functions for the discretization in space, and a Crank-Nicolson approach for the time stepping. We obtain a second-order error estimation in the H1 norm. Numerical experiments are performed to demonstrate the theoretical findings. 相似文献
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Monodisperse packing of disks in confined geometries is rarely addressed in the literature. We present some theoretical aspects of the microstructural properties of 2D static packing of disks between two concentric cylinders. In the core of the geometry, the packing is intact, while it is dilated in the vicinity of the walls as a result of the removal of overlapping disks. We have derived the formula for average packing density in concentric cylinders geometry with given ratio of the particle diameter to the gap between cylinders. It is verified and analyzed further by constructing ordered and disordered packs of monodisperse disks in computer. In this context, Voronoi tessellation is performed for the resulting packs to demonstrate the thickness of the static boundary layer where the packing is influenced by the presence of cylindrical walls. 相似文献