Immediate regularization of measure-type population densities in a two-dimensional chemotaxis systemwith signal consumption

This paper deals with the Neumann initial-boundary value problem for a classical chemotaxis system with signal consumption in a disk.In contrast to previous studies which have established a comprehensive theory of global classical solutions for suitably regular nonnegative initial data,the focus in the present work is on the question to which extent initially prescribed singularities can be regularized despite the presence of the nonlinear cross-diffusive interaction.The main result in this paper asserts that at least in the framework of radial solutions immediate regularization occurs under an essentially optimal condition on the initial distribution of the population density.More precisely,it will turn out that for any radially symmetric initial data belonging to the space of regular signed Borel measures for the population density and to L^(2) for the signal density,there exists a classical solution to the Neumann initial-boundary value problem,which is smooth and approaches the given initial data in an appropriate trace sense.

Comparative analysis of trade effects of anti-dumping measures targeting China vs.those initiated by China

Using the numbers of anti-dumping cases both in China and around the world, the value of imports and exports from 1995 to 2012, and the anti-dumping index (ADI) proposed by Finger and Murray in 1999, this paper analyzes the characteristics of anti-dumping measures that target China and those imposed by China, and constructs a multiple linear regression model. We try to show the effect of anti-dumping measures in either direction on the total value of China’s trade. This paper finds that both have great impact on export trade value. The intensity of the level of anti-dumping measures to which China is subject is positively correlated with total export value since this intensity, to a certain degree, can promote China’s industrial upgrading and the increase of the export of high value-added products. This paper further analyzes different effects of anti-dumping measures based on the method of technological content classification of Lall (2000). Finally, we put forward policy suggestions on how to enhance China’s export competitiveness by overcoming the effects of antidumping measures to which we are subject and by making proper use of antidumping measures on others.

On the Cauchy Problem of Evolution p-Laplacian Equation with Nonlinear Gradient Term

The authors study the existence of solution to p-Laplacian equation with nonlinear forcing term under optimal assumptions on the initial data, which are assumed to be measures. The existence of local solution is obtained.

Optimal Transportation for Generalized Lagrangian

This paper deals with the optimal transportation for generalized Lagrangian L = L（x, u, t）, and considers the following cost function： c（x, y） = inf x（0）=x x（1）=y u∈U∫0^1 L（x（s）, u（x（s）, s）, s）ds, where U is a control set, and x satisfies the ordinary equation x（s） = f（x（s）, u（x（s）, s））.It is proved that under the condition that the initial measure μ0 is absolutely continuous w.r.t. the Lebesgue measure, the Monge problem has a solution, and the optimal transport map just walks along the characteristic curves of the corresponding Hamilton-Jacobi equation：Vt（t, x） ＋ sup u∈U = 0,V（0, x） = Φ0（x）.