共查询到5条相似文献,搜索用时 15 毫秒
1.
Construction of Solutions and L^1-error Estimates of Viscous Methods for Scalar Conservation Laws with Boundary 总被引:4,自引:0,他引:4
Hong Xia LIU Tao PAN 《数学学报(英文版)》2007,23(3):393-410
This paper is concerned with an initial boundary value problem for strictly convex conservation laws whose weak entropy solution is in the piecewise smooth solution class consisting of finitely many discontinuities. By the structure of the weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux Nedelec, we give a construction method to the weak entropy solution of the initial boundary value problem. Compared with the initial value problem, the weak entropy solution of the initial boundary value problem includes the following new interaction type: an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary. According to the structure and some global estimates of the weak entropy solution, we derive the global L^1-error estimate for viscous methods to this initial boundary value problem by using the matching travelling wave solutions method. If the inviscid solution includes the interaction that an expansion wave collides with the boundary and the boundary reflects a new shock wave which is tangent to the boundary, or the inviscid solution includes some shock wave which is tangent to the boundary, then the error of the viscosity solution to the inviscid solution is bounded by O(ε^1/2) in L^1-norm; otherwise, as in the initial value problem, the L^1-error bound is O(ε| In ε|). 相似文献
2.
Some recent methods for solving second-order nonlinear
partial differential equations of divergence form and related
nonlinear problems are surveyed. These methods include entropy
methods via the theory of divergence-measure fields for
hyperbolic conservation laws, kinetic methods via kinetic
formulations for degenerate parabolichyperbolic equations, and
free-boundary methods via free-boundary iterations for
multidimensional transonic shocks for nonlinear equation of
mixed elliptic-hyperbolic type. Some recent trends in this
direction are also discussed.Dedicated to IMPA on the occasion of its 50th anniversary 相似文献
3.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):213-219
We prove that the δ-dimensional Bessel process (δ > 1) is a strong solution of a stochastic differential equation of the special form. The purpose of this paper is to investigate whether there exist other (weak and strong) solutions of these equations. This leads us to the conclusion that Zvonkin's theorem cannot be extended to stochastic differential equations with an unbounded drift. 相似文献
4.
5.
Ning Xu Huicheng Yin 《分析论及其应用》2005,21(2):176-187
In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz's inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal 相似文献