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It is shown that the two-component Camassa-Holm and Hunter-Saxton systems are geometrically integrable, namely they describe pseudo-spherical surfaces. As a consequence, their infinite number of conservation laws are directly constructed. In addition, a class of nonlocal symmetries depending on the pseudo-potentials are obtained. 相似文献
2.
Rainer BUCKDAHN 《应用数学学报(英文版)》2011,27(4):647-678
In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory
of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming principle for
the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward
way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper
and the lower Hamilton-Jacobi-Bellman-Isaacs equations with obstacles, respectively. The method differs significantly from
those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove
a new estimate for RBSDEs being sharper than that in the paper of El Karoui, Kapoudjian, Pardoux, Peng and Quenez (1997),
which turns out to be very useful because it allows us to estimate the L
p
-distance of the solutions of two different RBSDEs by the p-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution
to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs
equation with obstacle. 相似文献
3.
Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs's work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups. 相似文献
4.
In this paper, we present further development of the local discontinuous Galerkin (LDG) method designed in [21] and a new dissipative discontinuous Galerkin (DG) method for the HuntermSaxton equation. The numerical fluxes for the LDG and DG methods in this paper are based on the upwinding principle. The resulting schemes provide additional energy dissipation and better control of numerical oscillations near derivative singularities. Stability and convergence of the schemes are proved theoretically, and numerical simulation results are provided to compare with the scheme in [21]. 相似文献
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