完全非线性抛物型方程的整体解

本文所研究的是下列完全非线性抛物型方程的整体解:u_t=Δu+f(u,Du,D~2u),u(0)=u_0,其中,f∈C~(1+r),r>2/n,u_0属于介于 W_1~2(R~n)∩C~2(R~n)与 W_1~3(R~n)∩C~3(R~n) 间的中间空间,且充分小.从而推广了以往相应的工作.     

非线性Klein-Gordon方程柯西问题解的整体存在性与Blow-up

研究非线性Klein-Gordon方程的柯西问题u_(tt)-Δu+u=u|u|~(p-1),x∈R~n,t>0;u(x,0)=u_0(x),u_t(x,0)=u_1(x),x∈R~n.通过引进一族位势井,得到了解的整体存在性与不存在的门槛结果.     

退缩拟线性椭圆型方程某类边值问题的无穷多解

文[1]证明了如下D氏问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, u=0,x∈Ω存在非平凡解,本文讨论上述方程的另一类边界问题 -D_i(g|Du|~2)D_iu=f(x,u),x∈Ω, g(|Du|~2)D_iu(0)(n,x_i)+h(x,u)=0,x∈Ω, (1)其中Ω∈R~n是具有光滑边界的有界区域,n(x)是Ω在x点的外法向,D_iu=u/x_i,Du=gradu=u,重复指标表示求和,与问题(1)相应的泛函为:     

NON-RADIAL SOLUTIONS OF A SEMILINEAR ELLIPTIC EQUATION

In this paper we consider the eigenvalue problem of semilinear elliptic equation in R~n(n≥~3)-△u+α(x)u=λf(x, u), u∈H~1(R~n).     

Global well-posedness and blow-up for the hartree equation

For 2 γ min{4, n}, we consider the focusing Hartree equation iu_t+ △u +(|x|~(-γ)* |u|~2)u = 0, x ∈ R~n.(0.1)Let M [u] and E [u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of-△ Q + Q =(|x|~(-γ)* |Q|~2)Q. Guo and Wang [Z. Angew. Math.Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of(0.1) if M [u]~(1-s_c)E [u]~(s_c) M [Q]~(1-s_c)E [Q]~(s_c)(s_c=(γ-2)/2). In this paper, we consider the complementary case M [u]~(1-s_c)E [u]~(s_c)≥ M [Q]~(1-s_c)E [Q]~(s_c) and obtain a criteria on blow-up and global existence for the Hartree equation(0.1).     

Global Existence and Scattering in L2 for the Mass-critical Hartree Equation With H0,1 Initial Data

In this paper we consider the Cauchy Problem for the mass-critical Hartree equation I(e)tu △u=μ(|x|2*|u|2)u,(t,x)∈R×Rn,n≥3,(1) u(0,x)=φ(x), x∈Rn,(2)     

Scattering Versus Blowup Beyond the Mass-Energy Threshold for the Davey–Stewartson Equation in R~3

We study the Cauchy problem for the Davey–Stewartson equation i?_tu + Δu + |u|~2 u + E_1(|u|~2)u = 0,(t, x) ∈ R × R~3.The dichotomy between scattering and finite time blow-up shall be proved for initial data with finite variance and with mass-energy M(u_0)E(u_0) above the ground state threshold M(Q)E(Q).     

On Characterization of Poisson Integrals of Schrödinger Operators with Morrey Traces

Let L be a Schr?dinger operator of the form L =-Δ + V acting on L~2(R~n) where the nonnegative potential V belongs to the reverse H?lder class B_q for some q ≥ n. In this article we will show that a function f ∈ L~(2,λ)(R~n), 0 λ n, is the trace of the solution of L_u =-u_(tt) + L_u =0, u(x, 0) = f(x), where u satisfies a Carleson type condition sup x_B,r_Br_B~(-λ)∫_0~(rB)∫_(B(x_B,r_B))t|u(x,t)|~2dxdt≤C∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces L_L~(2,λ)(R~n) associated to the operator L, i.e.L_L~(2,λ)(R~n)=L~(2,λ)(R~n).Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L~(2,λ)(R~n) for all 0 λ n.     

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

§ 1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space W_t~2~(1,2)(O, +∞) into L_t~2~q(O, ∞), v>2. When v=N-1 we can get the radial solutions of problem where 2~*=2N/N-2 is the critical exponent of the Sobolev embedding H~1(R~n)→L~Q(R~N). Kurtz has discussed the existence of κ-node solution of (1.1), (1.2) for each κ∈N U{0} when the growth rate of |u|~(l-1)u+f(u) is lower then |u|~(v+3/v-1) i.e.     

Jacobian-determinant equation in the critical Besov spaces

Let Ω be a bounded domain in R~n with smooth boundary. Here we consider the following Jacobian-determinant equation det u(x)=f(x),x∈Ω;u(x)=x,x∈?Ω where f is a function on Ω with min_Ω f = δ 0 and Ωf(x)dx = |Ω|. We prove that if f ∈B_(p1)~(np)(Ω) for some p∈(n,∞), then there exists a solution u ∈ B_(p1)~(np+1)(Ω)C~1(Ω) to this equation. On the other hand, we give a simple example such that u ∈ C_0~1(R~2, R~2) while detu does not lie in B_(p1)~(2p)(R~2) for any p∞.     

Creep of polymer concrete in the nonlinear region

Two polyester-based polymer concretes with various volume content of diabase as an extender and aggregate are tested in creep under compression at different stress levels. The phenomenological and structural approaches are both used to analyze the experimental data. Common features of changes in the instantaneous and creep compliances are clarified, and a phenomenological creep model which accounts for the changes in the instantaneous compliance and in the retardation spectrum depending on the stress level is developed. It is shown that the model can be used to describe the experimental results of stress relaxation and creep under repeated loading. Modeling of the composite structure and subsequent solution of the optimization problem confirm the possibility of the existence of an interphase layer more compliant than the binder. A direct correlation between the interphase volume content and the instantaneous compliance of the composite is revealed. It is found that the distinction in nonlinearity of the viscoelastic behavior of the two polymer concretes under investigation can be due to the difference in their porosity. Submitted to the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000.) Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 147–164, 2000.     

Peridynamics via finite element analysis

Peridynamics is a recently developed theory of solid mechanics that replaces the partial differential equations of the classical continuum theory with integral equations. Since the integral equations remain valid in the presence of discontinuities such as cracks, the method has the potential to model fracture and damage with great generality and without the complications of mathematical singularities that plague conventional continuum approaches. Although a discretized form of the peridynamic integral equations has been implemented in a meshless code called EMU, the objective of the present paper is to describe how the peridynamic model can also be implemented in a conventional finite element analysis (FEA) code using truss elements. Since FEA is arguably the most widely used tool for structural analysis, this implementation may hasten the verification of peridynamics and significantly broaden the range of problems that the practicing analyst might attempt. Also, the present work demonstrates that different subregions of a model can be solved with either the classical partial differential equations or the peridynamic equations in the same calculation thus combining the efficiency of FEA with the generality of peridynamics. Several example problems show the equivalency of the FEA and the meshless peridynamic approach as well as demonstrate the utility and robustness of the method for problems involving fracture, damage and penetration.     

Variation of the structure and permeability of tensioned fiber layers during impregnation with a thermoplastic polymer melt

The influence of displacements of tensioned fibers on the impregnation of fibrous layers with a polymer melt and on the final composite structure is studied. Using computer simulation, it is shown that, during impregnation, the structure of tensioned fibrous layers changes considerably depending on the initial arrangement and tensioning of fibers. The consolidated regions formed under the melt front move inside the impregnated layer with the advancing melt front. Displacement of the tensioned fibers as well as the formation of “washouts” favors the impregnation of internal layers, but cause significant inhomogeneity of the polymer structure. The surface (on the side of the melt flow) regions are more saturated with the polymer than the internal ones. A difference in the melt percolation mechanisms at various impregnation regimes is revealed. The effective permeability coefficients of a tensioned fiber layer are not constant but depend on the conditions and regimes of impregnation. Submitted to the 11th Conference on the Mechanics of Composite Materials (Riga, June 11–15, 2000). Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 2, pp. 259–270, March–April, 2000.     

The Cauchy problem for ut=Δu+|∇u|

With q a positive real number, the nonlinear partial differential equation in the title of the paper arises in the study of the growth of surfaces. In that context it is known as the generalized deterministic KPZ equation. The paper is concerned with the initial-value problem for the equation under the assumption that the initial-data function is bounded and continuous. Results on the existence, uniqueness, and regularity of solutions are obtained.     

Price Expectations and Cobwebs Under Uncertainty

Classical approaches to location problems are based on the minimization of the average distance (the median concept) or the minimization of the maximum distance (the center concept) to the service facilities. The median solution concept is primarily concerned with the spatial efficiency while the center concept is focused on the spatial equity. The k-centrum model unifies both the concepts by minimization of the sum of the k largest distances. In this paper we investigate a solution concept of the conditional median which is a generalization of the k-centrum concept taking into account the portion of demand related to the largest distances. Namely, for a specified portion (quantile) of demand we take into account the entire group of the corresponding largest distances and we minimize their average. It is shown that such an objective, similar to the standard minimax, may be modeled with a number of simple linear inequalities. Equitable properties of the solution concept are examined.     

含有批处理机的三机流水作业加工总长问题在某些情形下的强NP困难性

本文研究含有批处理机的三台机器流水作业加工总长问题在某些情形下的计算复杂性。在批处理机上同时加工的工件组成一个工件批，一个工件批的所有工件同时开始、同时结束。当批处理机的容量有限时，我们证明了下列情形为强NP困难的：第一台机器是批处理机、其余两台机器是单机；第二台机器是单机、其余两台机器是批处理机；第三台机器是批处理机、其余两台机器是单机。     

A model for predicting the shear bearing capacity of FRP-strengthened beams

The shear failure of reinforced concrete beams needs more attention than the bending failure since no or only small warning precedes the failure. For this reason, it is of utmost importance to understand the shear bearing capacity and also to be able to undertake significant rehabilitation work if necessary. In this paper, a design model for the shear strengthening of concrete beams by using fiber-reinforced polymers (FRP) is presented, and the limitations of the truss model analogy are highlighted. The fracture mechanics approach is used in analyzing the bond behavior between the FRP composites and concrete. The fracture energy of concrete and the axial rigidity of the FRP are considered to be the most important parameters. The effective strain in the FRP when the debonding occurs is determined. The limitations of the anchorage length over the cross section are analyzed. A simple iterative design method for the shear debonding is finally proposed. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 3, pp. 357–372, May–June, 2008.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

Dynamical Spin Susceptibility in the t–J Model in the Superconducting Phase

Dynamical spin susceptibility is calculated for the t–J model in the superconducting phase using the memory function method in terms of the Hubbard operators. The self-consistent system of equations for the memory function is obtained within the mode-coupling approximation. Both itinerant hole excitations and localized spin fluctuations contribute to the memory function. Moreover, the itinerant contribution itself consists of two parts, i.e., the contribution of Bogoliubov quasiparticles and that of Cooper pairs. The spin dynamics is diffusive in the hydrodynamic limit, but the itinerant part does not contribute to the spin diffusion. In the high frequency region, spin–wave-like excitations continue to exist. We discuss our analytic results in the light of neutron scattering experiments performed on the cuprate superconductors.     

Gaussian Versus Optimal Integration of Analytic Functions

We consider error estimates for optimal and Gaussian quadrature formulas if the integrand is analytic and bounded in a certain complex region. First, a simple technique for the derivation of lower bounds for the optimal error constants is presented. This method is applied to Szeg?-type weight functions and ellipses as regions of analyticity. In this situation, the error constants for the Gaussian formulas are close to the obtained lower bounds, which proves the quality of the Gaussian formulas and also of the lower bounds. In the sequel, different regions of analyticity are investigated. It turns out that almost exclusively for ellipses, the Gaussian formulas are near-optimal. For classes of simply connected regions of analyticity, which are additionally symmetric to the real axis, the asymptotic of the worst ratio between the error constants of the Gaussian formulas and the optimal error constants is calculated. As a by-product, we prove explicit lower bounds for the Christoffel-function for the constant weight function and arguments outside the interval of integration. September 7, 1995. Date revised: October 25, 1996.