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Based on the characteristics and teaching practice of the course of "Linear Algebra", this paper introduces how to induction, summarize and reflection in the course of "Linear Algebra" through rich examples, so as to make the students better understand the concept and fully develop students' ability of problem analysis, problem-solving and innovation, and their mathematical literacy.

The well-posedness problem of anisotropic parabolic equation with variable exponents is studied in this paper. The weak solutions and the strong solutions are introduced, respectively. By a generalized Gronwall inequality, the stability of strong solutions to this equation is established, and the uniqueness of weak solutions is proved. Compared with the related works, a new boundary value condition, ∏ i = 1 N a i x , t = 0 , x , t ∈ ∂ Ω × 0 , T , is introduced the first time and has been proved that it can take place of the Dirichlet boundary value condition in some way.

In this paper, the existence and uniqueness of local solutions to the initial and boundary value problem of a class of parabolic system related to the p-Laplacian are studied. The regularization method is used to construct a sequence of approximation solutions, with the help of monotone iteration technique, then we get the existence of solution of a regularized system. By the use of a standard limiting process, the existence of the local solutions of the system is obtained. Finally, the uniqueness of the solution is also proven.

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