Professor Boling Guo, Academician of Chinese Academy of Sciences, born on October 23, 1936, in Longyan, Fujian, China, is now working in Beijing Institute of Applied Physics and Computational Mathematics (IAPCM). After four years' studies, he graduated from the department of mathematics, Fudan University in September, 1958. He was an assistant professor of this department after his graduation until January, 1963 when he joined the institute which he is now working in. He was first an assistant professor from February, 1963, to October, 1982, in IAPCM, then an associate professor from December, 1982, to October, 1987, and finally a professor from October, 1987 up to now. Professor Guo began to supervise Ph.D students in 1990.

We consider the partial regularity of weak solutions to the weighted Landau-Lifshitz flow on a 2-dimensional bounded smooth domain by Ginzburg-Landau type approximation. Under the energy smallness condition, we prove the uniform local C^∞ bounds for the approaching solutions. This shows that the approximating solutions are locally uniformly bounded in C^∞(Reg({u_∈})∩(\overline{\Omega}×R^+)) which guarantee the smooth convergence in these points. Energy estimates for the approximating equations are used to prove that the singularity set has locally finite two-dimensional parabolic Hausdorff measure and has at most finite points at each fixed time. From the uniform boundedness of approximating solutions in C^∞(Reg({u_∈})∩(\overline{\Omega}×R^+)), we then extract a subsequence converging to a global weak solution to the weighted Landau-Lifshitz flow which is in fact regular away from finitely many points.

In this article we study the global existence of solutions to an initial boundary value problem for the Mullins equation which describes the groove development at the grain boundaries of a heated polycrystal, both the Dirichlet and the Neumann boundary conditions are considered. For the classical solution we also investigate the large time behavior, it is proved that the solution converges to a constant, in the L^∞(Ω)-norm, as time tends to infinity.

For solving nonlinear parabolic equation on massive parallel computers, the construction of parallel difference schemes with simple design, high parallelism and unconditional stability and second order global accuracy in space, has long been desired. In the present work, a new kind of general parallel difference schemes for the nonlinear parabolic system is proposed. The general parallel difference schemes include, among others, two new parallel schemes. In one of them, to obtain the interface values on the interface of sub-domains an explicit scheme of Jacobian type is employed, and then the fully implicit scheme is used in the sub-domains. Here, in the explicit scheme of Jacobian type, the values at the points being adjacent to the interface points are taken as the linear combination of values of previous two time layers at the adjoining points of the inner interface. For the construction of another new parallel difference scheme, the main procedure is as follows. Firstly the linear combination of values of previous two time layers at the interface points among the sub-domains is used as the (Dirichlet) boundary condition for solving the sub-domain problems. Then the values in the sub- domains are calculated by the fully implicit scheme. Finally the interface values are computed by the fully implicit scheme, and in fact these calculations of the last step are explicit since the values adjacent to the interface points have been obtained in the previous step. The existence, uniqueness, unconditional stability and the second order accuracy of the discrete vector solutions for the parallel difference schemes are proved. Numerical results are presented to examine the stability, accuracy and parallelism of the parallel schemes.

In this paper we study an initial boundary value problem for a generalized complex Ginzburg-Landau equation with two spatial variables (2D). Applying the notion of the ε-regular map we show the unique existence of global solutions for initial data with low regularity and the existence of the global attractor.

We study the global nonexistence of the solutions of the nonlinear q-Laplacian wave equation u_{tt}-Δ_qu+(-Δ)^αu_t=|u|^{p-2}u, where 0 ‹ α ≤ 1, 2 ≤ q ‹ p. We obtain that the solution blows up in finite time if the initial energy is negative. Meanwhile, we also get the solution blows up in finite time with suitable positive initial energy under some conditions.

A In this paper, we employ both bifurcation method of dynamical systems and numerical exploration of differential equations to investigate the periodic waves of a general compressible hyperelastic rod equation u_t+3uu_x-u_{xxt}-ϒ(2u_xu_{xx}+uu_{xxx})=0, with parameter ϒ ‹ 0. New expressions including explicit expressions and implicit expressions are obtained. Some previous results are extended. Specially, a new phenomenon is found: when the initial value tends to a certain number, the periodic shock wave suddenly changes into a smooth periodic wave. In dynamical systems, this represents that one of orbits can pass through the singular line. The coherency of numerical simulation and theoretical derivation implies the correctness of our results.