Published in Acta Mathematica Scientia
In this article, by the mean-integral of the conserved quantity, we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region. Moreover, we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process. Finally, we p...
Published in Acta Mathematica Scientia
In this article, two results concerning the periodic points and normality of meromorphic functions are obtained: (i) the exact lower bound for the numbers of periodic points of rational functions with multiple fixed points and zeros is proven by letting R(z) be a non-polynomial rational function, and if all zeros and poles of R(z) − z are multiple,...
Published in Acta Mathematica Scientia
We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymp...
Published in Acta Mathematica Scientia
In this article, we study the pointwise estimates of solutions to the nonlinear viscous wave equation in even dimensions (n ≥ 4). We use the Green’s function method. Our approach is on the basis of the detailed analysis of the Green’s function of the linearized system. We show that the decay rates of the solution for the same problem are different ...
Published in Acta Mathematica Scientia
In this paper, we study the generalized lower order of entire functions defined by Dirichlet series. By constructing the Newton polygon based on Knopp-Kojima’s formula, we obtain a relation between the coefficients of the Dirichlet series and its generalized lower order.
Published in Acta Mathematica Scientia
In 1965 Baker first considered the distribution of Julia sets of transcendental entire maps and proved that the Julia set of an entire map cannot be contained in any finite set of straight lines. In this paper we shall consider the distribution problem of Julia sets of meromorphic maps. We shall show that the Julia set of a transcendental meromorph...
Published in Acta Mathematica Scientia
We establish uniqueness theorems of L-functions in the extended Selberg class, which show how an L-function and a meromorphic function are uniquely determined by their shared values in two finite sets. This can be seen as a new solution of a problem proposed by Gross.
Published in Acta Mathematica Scientia
We study the single projection algorithm of Tseng for solving a variational inequality problem in a 2-uniformly convex Banach space. The underline cost function of the variational inequality is assumed to be monotone and Lipschitz continuous. A weak convergence result is obtained under reasonable assumptions on the variable step-sizes. We also give...
Published in Acta Mathematica Scientia
In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model. Different from others studies, we consider the physical case that the mobilities of the charges are different. The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-sc...
Published in Acta Mathematica Scientia
We consider a Neumann problem driven by the (p, q)-Laplacian under the Landesman-Lazer type condition. Using the classical saddle point theorem and other classical results of the calculus of variations, we show that the problem has at least one nontrivial weak solution.
