QUALITATIVE ANALYSIS OF BOBWHITE QUAIL POPULATION MODEL

In this paper, the qualitative behavior of solutions of the bobwhite quail pop-ulation modelwhere 0   

动态投入产出系统的稳定性分析

The dynamic input-output model is well known in economic theory and practice. In this paper, the asymptotic stability and balanced growth solutions of the dynamic input-output system are considered. Under some natural assumptions which do not require the technical coefficient matrix to be indecomposable,it has been proved that the dynamic input-output system is not asymptotically stable and the closed dynamic input-output model has a balanced growth solution.     

Asymptotic Behavior of a Structure Made by a Plate and a Straight Rod

This paper is devoted to describing the asymptotic behavior of a structure made by a thin plate and a thin perpendicular rod in the framework of nonlinear elasticity. The authors scale the applied forces in such a way that the level of the total elastic energy leads to the Von-K′arm′an’s equations (or the linear model for smaller forces) in the plate and to a one-dimensional rod-model at the limit. The junction conditions include in particular the continuity of the bending in the plate and the stretching in the rod at the junction.     

ON INTERACTION OF SHOCK AND SOUND WAVE （I）

This paper studies the interaction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged dormain, By using the method of constructing asymptotic solutions and Newton‘siteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will he given in the following paper.     

The Brio System with Initial Conditions Involving Dirac Masses: A Result Afforded by a Distributional Product

The Brio system is a 2 × 2 fully nonlinear system of conservation laws which arises as a simplified model in the study of plasmas. The present paper offers explicit solutions to this system subjected to initial conditions containing Dirac masses. The concept of a solution emerges within the framework of a distributional product and represents a consistent extension of the concept of a classical solution. Among other features, the result shows that the space of measures is not sufficient to contain all solutions of this problem.     

Finite Integral Transform Solutions for Free Vibrations of Rectangular Thin Plates With Mixed Boundary Constraints北大核心CSCD

Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

EXISTENCE OF GENERALIZED SOLUTIONS TO A HYPERBOLIC MODEL OF COMBUSTION

In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.     

EXISTENCE AND REGULARITY OF SOLUTIONS TO MODEL FOR LIQUID MIXTURE OF ^3HE-^4HE

Existence and regularity of solutions to model for liquid mixture of 3He-4He is considered in this paper.First,it is proved that this system possesses a unique global weak solution in H 1(,C × R) by using Galerkin method.Secondly,by using an iteration procedure,regularity estimates for the linear semigroups,it is proved that the model for liquid mixture of 3He-4He has a unique solution in Hk(,C × R) for all k ≥ 1.     

Local solvability of the k-Hessian equations

We give a classification of second-order polynomial solutions for the homogeneous k-Hessian equation σ_k[u] = 0. There are only two classes of polynomial solutions: One is convex polynomial; another one must not be(k + 1)-convex, and in the second case, the k-Hessian equations are uniformly elliptic with respect to that solution. Based on this classification, we obtain the existence of C∞local solution for nonhomogeneous term f without sign assumptions.     

THE CHARACTERISTIC FINITE DIFFERENCE METHOD FOR THREE-DIMENSIONAL MOVING BOUNDARY VALUE PROBLEM

The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be discribed as a coupled system of nonlinear partial differential equations with moving boundary value problem. For a generic case of the three-demensional bounded region, bi this thesis, the effects of gravitation、buoyancy and capillary pressure are considered, we put forward a kind of characteristic finite difference schemes and make use thick and thin grids to form a complete set, and of calculus of vaviations, the change of variable, the theory of prior estimates and techniques, Optimal order estimates in l~2 norm are derived for the error in approximate assumption, Thus we have completely solved the well-known theoretical problem proposed by J. Douglas, Jr.     

Piecewise linear approximation for the dynamical Φ_3~4 model

We construct a piecewise linear approximation for the dynamicalΦ3~4 model on T^3.The approximation is based on the theory of regularity structures developed by Hairer(2014).They proved that renormalization in a dynamicalΦ3~4 model is necessary for defining the nonlinear term.In contrast to Hairer(2014),we apply piecewise linear approximations to space-time white noise,and prove that the solutions of the approximating equations converge to the solution of the dynamicalΦ_3~4 model.In this case,the renormalization corresponds to multiplying the solution by a t-dependent function,and adding it to the approximating equation.     

EXISTENCE OF POSITIVE SOLUTIONS TO SEMILINEAR ELLIPTIC SYSTEMS IN IRN WITH ZERO MASS

In this paper, we prove the existence of at least one positive solution pairto the following semilinear elliptic systemby using a linking theorem, where K（x）is a positive function in L^s（R^N） for some s 〉 1and the nonnegative functions f, g ∈ C（R, R） are of quasicritical growth, superlinear atinfinity. We do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as a partial extension of a recent result of Alves, Souto and Montenegro in [1] concerning the existence of a positive solution to the following semilinear elliptic problemand a recent result of Li and Wang in [22] concerning the existence of nontrivial solutions to a semilinear elliptic system of Hamiltonian type in R^N.     

Approximation Solutions of Nonlinear Strongly Accretive Operator Equations by Ishikawa Iteration Procedure with Errors

Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~' c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.     

On the Nonlinear Matrix Equation X+ A *f1（X）A +B*f2（X）B=Q

In this paper, nonlinear matrix equations of the form X + A*f1 (X)A + B*f2 (X)B = Q are discussed. Some necessary and sufficient conditions for the existence of solutions for this equation are derived. It is shown that under some conditions this equation has a unique solution, and an iterative method is proposed to obtain this unique solution. Finally, a numerical example is given to identify the efficiency of the results obtained.     

具有一般终端时刻和非一致线性增长生成元的倒向随机微分方程的$L^p$解

In this paper, we establish the existence of the minimal L~p(p 1) solution of backward stochastic differential equations(BSDEs) where the time horizon may be finite or infinite and the generators have a non-uniformly linear growth with respect to t. The main idea is to construct a sequence of solutions {(Y~n, Z~n)} which is a Cauchy sequence in S~p× M~p space, and finally we prove {(Y~n, Z~n)} converges to the L~p(p 1) solution of BSDEs.     

Mathematical modeling and numerical simulation of telephone cord buckles of elastic films

An annular sector model for the telephone cord buckles of elastic thin films on rigid substrates is established, in which the von Krman plate equations in polar coordinates are used for the elastic thin film and a discrete version of the Griffith criterion is applied to determine the shape and scale of the parameters. A numerical algorithm combining the Newmark-β scheme and the Chebyshev collocation method is designed to numerically solve the problem in a quasi-dynamic process. Numerical results are presen...     

Rate of strong consistency of quasi maximum likelihood estimate in generalized linear models

Under the assumption that in the generalized linear model (GLM) the expectation of the response variable has a correct specification and some other smooth conditions, it is shown that with probability one the quasi-likelihood equation for the GLM has a solution when the sample size n is sufficiently large. The rate of this solution tending to the true value is determined. In an important special case, this rate is the same as specified in the LIL for iid partial sums and thus cannot be improved anymore.     

Quasi-hydrostatic Primitive Equations for Ocean Global Circulation Models

Global existence of weak and strong solutions to the quasi-hydrostatic primitive equations is studied in this paper. This model, that derives from the full non-hydrostatic model for geophysical fluid dynamics in the zero-limit of the aspect ratio, is more realistic than the classical hydrostatic model, since the traditional approximation that consists in neglecting a part of the Coriolis force is relaxed. After justifying the derivation of the model, the authors provide a rigorous proof of global existence of weak solutions, and well-posedness for strong solutions in dimension three.     

Dirac Concentrations in a Chemostat Model of Adaptive Evolution

This paper deals with a non-local parabolic equation of Lotka-Volterra type that describes the evolution of phenotypically structured populations.Nonlinearities appear in these systems to model interactions and competition phenomena leading to selection.In this paper,the equation on the structured population is coupled with a differential equation on the nutrient concentration that changes as the total population varies.Different methods aimed at showing the convergence of the solutions to a moving Dirac mass are reviewed.Using either weak or strong regularity assumptions,the authors study the concentration of the solution.To this end,BV estimates in time on appropriate quantities are stated,and a constrained Hamilton-Jacobi equation to identify where the solutions concentrates as Dirac masses is derived.     

有关M.S.Berger问题的注记

In this paper, we discuss the problem concerning global and local structure of solutions of an operator equation posed by M. S. Berger. Let f : U 真包含 E → F be a C1 map, where E and F are Banach spaces and U is open in E. We show that the solution set of the equation f(x) = y for a fixed generalized regular value y of f is represented as a union of disjoint connected C1 Banach submanifolds of U, each of which has a dimension and its tangent space is given. In particular, a characterization of the isolated solutions of the equation f(x) = y is obtained.