In his unremitting efforts to train mathematics talents, Professor Gu has greatly helped to bring up a large number of students, leading them onto their own way of mathematical research. Now many of them have become leaders or the backbone force in their respective departments and special areas. Because of his significant contributions to the educational cause of China, Professor Gu has been awarded many honors and titles such as the national advanced worker in 1956, a national labor model of the education in 1993, etc. Moreover, some university textbooks written by him with his group have received prizes for excellence from the state.

In this paper we discuss a Cauchy problem for nonlinear wave equation with delta initial data, including delta impulse and/or delta displacement. The solution of the Cauchy problem in appropriate sense is given. Meanwhile, the singularity structure of the solution is also described.

In this paper, we consider the Cauchy problem for two dimensional Landau-Lifshitz equation on 2-dimenslonal Riemannian manifold M without boundary. We proved that if u: M × R_+ → S², is a weak solution, then u is unique and smooth on M × R_+ with the exception of finitely many points.

We discuss the existence of global solutions to a fluid dynamic model for materials of Korteweg type, and discuss the three dimensional nonisothermal motion. The higher order derivatives of density in the constitutive relation makes it necessary to introduce an interstitial working term in the energy equation. This makes the energy estimate more involved. Nevertheless, it is possible to show the existence of global solutions by the euergy method.

With the aid of the nonhomogeneous Calderon-Zygmund decomposition the present paper studies the L^p estimates for a class of integral operators related to the boundary value problems of degenerate elliptic equations. The method used here is also applicable to general evolution equations of elliptic type.

In this paper, we discretize the generalized Ginzburg-Landau equations with the periodic boundary condition by the finite difference method in spatial direction. It is proved that for each mesh size, there exist at tractors for the discretized systems. The bounds for the Hausdorff dimensions of the discrete attractors are obtained, and the various bounds are independtmt of tho mesh sizes.