In this paper the techniques of nonstandard analysis are used to establish the quasi-Duhamel Principle. The applications of our result lead to simple nonstandard proofs for some theorems of classical mathematical anal...In this paper the techniques of nonstandard analysis are used to establish the quasi-Duhamel Principle. The applications of our result lead to simple nonstandard proofs for some theorems of classical mathematical analysis.This principle is also very useful for nonstandard asymptotic approximation of sums and integrals.展开更多
This paper deals with an attraction-repulsion chemotaxis model(ARC) in multi-dimensions. By Duhamel's principle, the implicit expression of the solution to(ARC)is given. With the method of Green's function, th...This paper deals with an attraction-repulsion chemotaxis model(ARC) in multi-dimensions. By Duhamel's principle, the implicit expression of the solution to(ARC)is given. With the method of Green's function, the authors obtain the pointwise estimates of solutions to the Cauchy problem(ARC) for small initial data, which yield the W s,p(1 ≤p≤∞) decay properties of solutions.展开更多
文摘In this paper the techniques of nonstandard analysis are used to establish the quasi-Duhamel Principle. The applications of our result lead to simple nonstandard proofs for some theorems of classical mathematical analysis.This principle is also very useful for nonstandard asymptotic approximation of sums and integrals.
基金supported by the National Natural Science Foundation of China(No.11171213)supported by the National Natural Science Foundation of China(No.11231006)the National Research Foundation for the Doctoral Program of Higher Education of China(No.20130073110073)
文摘This paper deals with an attraction-repulsion chemotaxis model(ARC) in multi-dimensions. By Duhamel's principle, the implicit expression of the solution to(ARC)is given. With the method of Green's function, the authors obtain the pointwise estimates of solutions to the Cauchy problem(ARC) for small initial data, which yield the W s,p(1 ≤p≤∞) decay properties of solutions.
