Published in Acta Mathematica Scientia
This work consider boundary integrability of the weak solutions of a non-Newtonian compressible fluids in a bounded domain in dimension three, which has the constitutive equations as S=−P(ϱ)+2μ0(1+|Dd(u)|2)(p−2)/2Dd(u)+cdivu(1−ca|divu|a)1/aII.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{a...
Published in Acta Mathematica Scientia
In this paper, we study the existence of nontrivial radial convex solutions of a singular Dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theorem in cones. We deal with more general nonlinear term than those in the literature.
Published in Acta Mathematica Scientia
In this paper, we investigate non-zero positive eigenvalues of the Laplacian with Dirichlet boundary condition in an n-dimentional Euclidean space ℝn, then we obtain an new upper bound of the (k + 1)-th eigenvalue λk+1, which improve the previous estimate which was obtained by Cheng and Yang, see (1.8).
Published in Acta Mathematica Scientia
In this paper, we establish the following limiting weak-type behaviors of Littlewood-Paley g-function g': for nonnegative function f ∈ L1(Rn), limλ→0+λm({x∈ℝn:|gφf(x)|>λ})=m({x∈ℝn:(∫0∞|φr(x)|2drr)1/2>1})‖f‖1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepack...
Published in Acta Mathematica Scientia
In this paper, we consider the problem of delay-dependent stability for state estimation of neural networks with two additive time–varying delay components via sampled-data control. By constructing a suitable Lyapunov–Krasovskii functional with triple and four integral terms and by using Jensen’s inequality, a new delay-dependent stability criterio...
Published in Acta Mathematica Scientia
The Riemann problem for the chromatography equations in a conservative form is considered. The global solution is obtained under the assumptions that the initial data are taken to be three piecewise constant states. The wave interaction problems are discussed in detail during the process of constructing global solutions to the perturbed Riemann pro...
Published in Acta Mathematica Scientia
We consider entire solutions u of the equations describing the stationary flow of a generalized Newtonian fluid in 2D concentrating on the question, if a Liouville-type result holds in the sense that the boundedness of u implies its constancy. A positive answer is true for p-fluids in the case p > 1 (including the classical Navier-Stokes system for...
Published in Acta Mathematica Scientia
Let W = (Wt)t≥0 be a supercritical α-stable Dawson-Watanabe process (with α ∈ (0, 2]) and f be a test function in the domain of −(-Δ)α/2 satisfying some integrability condition. Assuming the initial measure W0 has a finite positive moment, we determine the long-time asymptotic of arbitrary order of Wt(f). In particular, it is shown that the local b...
Published in Acta Mathematica Scientia
In this article, we mainly study the invariance of some biholomorphic mappings with special geometric characteristics under the extension operators. First we generalize the Roper-Suffridge extension operators on Bergman-Hartogs domains. Then, by the geometric characteristics of subclasses of biholomorphic mappings, we conclude that the modified Rop...
Published in Acta Mathematica Scientia
In this paper, we are concerned with the existence of mild solution and controllability for a class of nonlinear fractional control systems with damping in Hilbert spaces. Our first step is to give the representation of mild solution for this control system by utilizing the general method of Laplace transform and the theory of (α, γ)-regularized fa...
