A class of alternating group explicit iterative method using the C-N scheme is derived for solving four order parabolic equations, and the analysis for convergency is given. In the end, the numerical result is given, which shows the iterative method is convergent, high precision, and is suitable for parallel computing. 1 Preface In Science and engineering computing, parabolic equations are impo...

J. Reine Angew. Math 436 (1993), pp. 209– 219. Stony Brook IMS Preprint #1991/23 December 1991 Let G ⊂ PSL(2,C) be a geometrically finite Kleinian group, with region of discontinuity Ω(G). By Ahlfors’ finiteness theorem, the quotient, Ω(G)/G, is a finite union of Riemann surfaces of finite type. Thus on it, there are only finitely many mutually disjoint free homotopy classes of simple closed cu...

This study describes the effects of bounce, brake, and roll behavior of a bus toward its leaf spring suspension systems. Parabolic leaf springs are designed based on vertical deflection and stress; however, loads are practically derived from various modes especially under harsh road drives or emergency braking. Parabolic leaf springs must sustain these loads without failing to ensure bus and pa...

For a semisimple Lie group G with parabolic subgroups Q ⊂ P ⊂ G, we associate to a parabolic geometry of type (G,P ) on a smooth manifold N the correspondence space CN , which is the total space of a fiber bundle over N with fiber a generalized flag manifold, and construct a canonical parabolic geometry of type (G,Q) on CN . Conversely, for a parabolic geometry of type (G,Q) on a smooth manifol...

In this paper, we expand circular arc triangulations with parabolic arcs, which are triangulations whose edges are circular or parabolic arcs. Creating triangulations this way bears several advantages if angles are to be optimized, especially for finite element method. A typical reason for the occurrence of small angles in a straight line triangulation is that the geometry of the vertex set for...

We formulate a quasilinear parabolic equation describing the behavior of global-in-time solution to semilinear equation. study this in accordance with blow-up and quenching patterns original This is new theory partial differential equations presents several difficulties for mathematical analysis. Two approaches are examined: functional analysis viscosity solution.

The chains studied in this paper generalize Chern–Moser chains for CR structures. They form a distinguished family of one dimensional submanifolds in manifolds endowed with a parabolic contact structure. Both the parabolic contact structure and the system of chains can be equivalently encoded as Cartan geometries (of different types). The aim of this paper is to study the relation between these...

Hölder estimates for spatial second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.

Let X be a mixture of independent Brownian motion and symmetric stable process. In this paper we establish sharp bounds for transition density of X, and prove a parabolic Harnack inequality for nonnegative parabolic functions of X.