AN ANALYTICAL SOLUTION OF TRANSVERSE VIBRATION OF RECTANGULAR PLATES SIMPLY SUPPORTED AT TWO OPPOSITE EDGES WITH ARBITRARY NUMBER OF ELASTIC LINE SUPPORTS IN ONE WAY

ＡＮＡＮＡＬＹＴＩＣＡＬＳＯＬＵＴＩＯＮＯＦＴＲＡＮＳＶＥＲＳＥＶＩＢＲＡＴＩＯＮＯＦＲＥＣＴＡＮＧＵＬＡＲＰＬＡＴＥＳＳＩＭＰＬＹＳＵＰＰＯＲＴＥＤＡＴＴＷＯＯＰＰＯＳＩＴＥＥＤＧＥＳＷＩＴＨＡＲＢＩＴＲＡＲＹＮＵＭＢＥＲＯＦＥＬＡＳＴＩＣＬＩＮＥ...     

FORCED OSCILLATIONS OF BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FUNCTIONAL PARTIAL DIFFERENTIAL EQUATIONS

ＦＯＲＣＥＤＯＳＣＩＬＬＡＴＩＯＮＳＯＦＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＨＩＧＨＥＲＯＲＤＥＲＦＵＮＣＴＩＯＮＡＬＰＡＲＴＩＡＬＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＪｉｎＭｉｎｇＺｈｏｎｇ（靳明忠），ＤｏｎｇＹｉｎｇ（董莹），Ｌｉ...     

THE EXISTENCE OF PERIODIC SOLUTION OF THE FOURTH ORDINARY NONLINEAR DIFFERENTIAL EQUATION CAUSED BY FLOW－IN

ＴＨＥＥＸＩＳＴＥＮＣＥＯＦＰＥＲＩＯＤＩＣＳＯＬＵＴＩＯＮＯＦＴＨＥＦＯＵＲＴＨＯＲＤＩＮＡＲＹＮＯＮＬＩＮＥＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＣＡＵＳＥＤＢＹＦＬＯＷ－ＩＮＤＵＣＥＤＶＩＢＲＡＴＩＯＮＧｕＱｉｎｇ－ｆａｎｇ（顾清芳）Ｔａ...     

SINGULAR PERTURBATION OF INITIAL BOUNDARY VALUE FROBLEMS OF REACTION DIFFUSlON EQUATION WITH DELAY

ＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＯＦＩＮＩＴＩＡＬＢＯＵＮＤＡＲＹＶＡＬＵＥＦＲＯＢＬＥＭＳＯＦＲＥＡＣＴＩＯＮＤＩＦＦＵＳｌＯＮＥＱＵＡＴＩＯＮＷＩＴＨＤＥＬＡＹＺｈａｎｇＸｉａｎｇ（张祥）（ＡｎｈｕｉＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ）Ｗｕ...     

EXISTENCE OF SOLUTIONS OF THREE－POINT BOUNDARY VALUE PROBLEMS FOR NONLINEAR FOURTH ORDER DIFFERENTIAL EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＳＯＬＵＴＩＯＮＳＯＦＴＨＲＥＥ－ＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＦＯＲＮＯＮＬＩＮＥＡＲＦＯＵＲＴＨＯＲＤＥＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮ￥ＧａｏＹｏｎｇｘｉｎ（高永馨）（Ｄｅｐａｒｔｍｅｎｔｏ...     

BLOW－UP AND DIE－OUT OF SOLUTIONS OF NONLINEAR PSEUDO-HYPERBOLIC EQUATIONS OF GENERALIZED NERVE CONDUCTION TYPE

ＢＬＯＷ－ＵＰＡＮＤＤＩＥ－ＯＵＴＯＦＳＯＬＵＴＩＯＮＳＯＦＮＯＮＬＩＮＥＡＲＰＳＥＵＤＯＨＹＰＥＲＢＯＬＩＣＥＱＵＡＴＩＯＮＳＯＦＧＥＮＥＲＡＬＩＺＥＤＮＥＲＶＥＣＯＮＤＵＣＴＩＯＮＴＹＰＥＷａｎｇＦａｎｂｉｎ（王凡彬）（ＲｅｃｅｉｖｅｄＪｕｎｅ２...     

UNCONDITIONAL STABLE SOLUTIONS OF THE EULER EQUATIONS FOR TWO－AND THREE－D WINGS IN ARBITRARY MOTION

ＵＮＣＯＮＤＩＴＩＯＮＡＬＳＴＡＢＬＥＳＯＬＵＴＩＯＮＳＯＦＴＨＥＥＵＬＥＲＥＱＵＡＴＩＯＮＳＦＯＲＴＷＯ－ＡＮＤＴＨＲＥＥ－ＤＷＩＮＧＳＩＮＡＲＢＩＴＲＡＲＹＭＯＴＩＯＮＧａｏＺｈｅｎｇｈｏｎｇ（高正红）（ＲｅｃｅｉｖｅｄＪａｎ．１２,１９９５,Ｃ...     

NUMERICAL SIMULATION OF THREE DIMENSIONAL TURBULENT FLOW IN SUDDENLY EXPANDED RECTANGULAR DUCT

ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＴＵＲＢＵＬＥＮＴＦＬＯＷＩＮＳＵＤＤＥＮＬＹＥＸＰＡＮＤＥＤＲＥＣＴＡＮＧＵＬＡＲＤＵＣＴＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＴＨＲＥＥＤＩＭＥＮＳＩＯＮＡＬＴＵＲＢＵ...     

STRESS－STBAIN FIELD NEAR CRACK TIP AND CALCULATION OF CRITICAL STRESS OF CRACK PROPAGATION IN A PURE BENDING BEAM OF RECTANGULAR SECTION WITH ONE－SIDED MODEICRACK

ＳＴＲＥＳＳ－ＳＴＢＡＩＮＦＩＥＬＤＮＥＡＲＣＲＡＣＫＴＩＰＡＮＤＣＡＬＣＵＬＡＴＩＯＮＯＦＣＲＩＴＩＣＡＬＳＴＲＥＳＳＯＦＣＲＡＣＫＰＲＯＰＡＧＡＴＩＯＮＩＮＡＰＵＲＥＢＥＮＤＩＮＧＢＥＡＭＯＦＲＥＣＴＡＮＧＵＬＡＲＳＥＣＴＩＯＮＷＩＴＨＯＮＥ－Ｓ...     

EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS OF SECOND ORDER NONLINEAR EQUATION

ＥＸＩＳＴＥＮＣＥＯＦＰＯＳＩＴＩＶＥＳＯＬＵＴＩＯＮＳＦＯＲＡＣＬＡＳＳＯＦＳＩＮＧＵＬＡＲＴＷＯＰＯＩＮＴＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭＳＯＦＳＥＣＯＮＤＯＲＤＥＲＮＯＮＬＩＮＥＡＲＥＱＵＡＴＩＯＮ（杨作东）ＥＸＩＳＴＥＮＣＥＯＦＰＯＳ...     

Singular perturbation of boundary value problem for a vector fourth order nonlinear differential equation

We study the vector boundary value problem with boundary perturbations: ε~2y~((4))=f(x,y,y″,ε, μ) ( μ<χ<1-μ) y(χ,ε,μ)l_(χ-μ)= A_1(ε,μ), y(χ,ε,μ)l_(χ-1-μ)=B_1(ε,μ) y″(χ,ε,μ)l_(χ-μ)=A_2(ε,μ),y″(χ,ε,μ)l_(χ-1-μ)=B_2(ε,μ)where yf, A_j and B_j (j=1,2) are n-dimensional vector functions and ε,μ are two small positive parameters. This vector boundary value problem does not appear to have been studied, although the scalar boundary value problem has been treated. Under appropriate assumptions, using the method of differential inequalities we find a solution of the vector boundary value problem and obtain the uniformly valid asymptotic expansions.     

Darboux problem for a differential equation with fractional derivative

We find conditions for the unique solvability of the problem u _xy (x, y) = f(x, y, u(x, y), (D ₀ ^r u)(x, y)), u(x, 0) = u(0, y) = 0, x ∈ [0, a], y ∈ [0, b], where (D ₀ ^r u)(x, y) is the mixed Riemann-Liouville derivative of order r = (r ₁, r ₂), 0 < r ₁, r ₂ < 1, in the class of functions that have the continuous derivatives u _xy (x, y) and (D ₀ ^r u)(x, y). We propose a numerical method for solving this problem and prove the convergence of the method. __________ Translated from Neliniini Kolyvannya, Vol. 8, No. 4, pp. 456–467, October–December, 2005.     

On an analogue of the Euler-Cauchy polygon method for the numerical solution of ux y = f(x,y, u,ux, uy)

This paper develops, with an eye on the numerical applications, an analogue of the classical Euler-Cauchy polygon method (which is used in the solution of the ordinary differential equation dy/dx=f(x, y), y(x ₀)=y ₀) for the solution of the following characteristic boundary value problem for a hyperbolic partial differential equation u _xy =f(x, y, u, u _x , y _y ), u(x, y ₀)=(x), u(x ₀, y)=(y), where (x ₀)=(y ₀). The method presented here, which may be roughly described as a process of bilinear interpolation, has the advantage over previously proposed methods that only the tabulated values of the given functions (x) and (y) are required for its numerical application. Particular attention is devoted to the proof that a certain sequence of approximating functions, constructed in a specified way, actually converges to a solution of the boundary value problem under consideration. Known existence theorems are thus proved by a process which can actually be employed in numerical computation.

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The asymptotic expansions of singularly perturbed boundary value problems

In this paper we study the singularly perturbed boundary value problem:εy″=f(t,y,ε),y(0)=ξ(ε),y(1)=η(ε).where εis a positive small parameter.In the conditions:f_(?)(0,y,0)≥m_0 ,f_(?)(l,y,0)≥m_0 and f_(?)f(t,y,ε)≥0 ,we prove the existences,and uniformly valid asymptotic expansions of solutions for the given boundary value problems,and hence we improve the existing results.     

On the free energy and variational theorem of elastic problem in thermal shock

In some investigations on variational principle for coupled thermoelastic problems, the free energy Φ(e_ij,θ) ,where the state variables are elastic strain e_ij and temperature increment θ, is expressed as Φ(e_ij,θ)=λ/2e_kke_ij=ue_k1e_k1-γe_kkθ-c/2 p θ²/T₀(0.1) This expression is employed only under the condition of |θ|≤T₀(absolute temperature of reference) But the value of temperature increment is great, even greater than T₀ in thermal shock. And the material properties (λ ,μ ,ν ,c , etc.) will not remain constant, they vary with θ. The expression of free energy for this condition.is derived in this paper. Equation (0.1) is its special case.Euler’s equations will be nonlinear while this expression of free energy has been introduced into variational theorem. In order to linearise, the time interval of thermal shock is divided into a number of time elements Δt_k, (Δt_k=t_k-t_k-1,k=1,2…,n), which are so small that the temperature increment θ_k within it is very small, too. Thus, the material properties may be defined by temperature field T_k-1=T(x₁,x₂,x₃,t_k-1) at instant t_k-1 , and the free energy Φ_k expressed by eg. (0.1) may be employed in element Δt_k.Hence the variational theorem will be expressed partly and approximately.     

Oscillation criteria for a second-order quasilinear neutral functional dynamic equation on time scales

Our aim is to establish some sufficient conditions for the oscillation of the second-order quasilinear neutral functional dynamic equation

On nonlinear problems of mixed type: A qualitative theory using infinite-dimensional center manifolds

We consider the equation a(y)u_xx+div_y(b(y)_yu)+c(y)u=g(y, u) in the cylinder (–l,l)×, being elliptic where b(y)>0 and hyperbolic where b(y)<0. We construct self-adjoint realizations in L₂() of the operatorAu= (1/a) div_y(b_yu)+(c/a) in the case ofb changing sign. This leads to the abstract problem u_xx+Au=g(u), whereA has a spectrum extending to + as well as to –. For l= it is shown that all sufficiently small solutions lie on an infinite-dimensional center manifold and behave like those of a hyperbolic problem. Anx-independent cross-sectional integral E=E(u, u_x) is derived showing that all solutions on the center manifold remain bounded forx ±. For finitel, all small solutionsu are close to a solution on the center manifold such that u(x)-(x) Ce ^-(1-|x|) for allx, whereC and are independent ofu. Hence, the solutions are dominated by hyperbolic properties, except close to the terminal ends {±1}×, where boundary layers of elliptic type appear.     

A unified approach to closed-form solutions of moving heat-source problems

A closed-form model for the computation of temperature distribution in an infinitely extended isotropic body with a time-dependent moving-heat sources is discussed. The temperature solutions are presented for the sources of the forms: (i) ₀₁(t)=₀ exp(−λt), (ii) ₀₂(t) =₀(t/t ^*)exp(−λt), and ₀₃(t)=₀[1+a cos(ωt)], where λ and ω are real parameters and t ^* characterizes the limiting time. The reduced (or dimensionless) temperature solutions are presented in terms of the generalized representation of an incomplete gamma function Γ(α,x;b) and its decomposition C _Γ and S _Γ. The solutions are presented for moving, -point, -line, and -plane heat sources. It is also demonstrated that the present analysis covers the classical temperature solutions of a constant strength source under quasi-steady state situations. Received on 13 June 1997     

Ergodicity of minimal sets in scalar parabolic equations

Skew product semiflowΠ _t :X ×Y → X × Y generated by $$\left\{ \begin{gathered} u_t = u_{xx} + f(y \cdot t,x,u,u_x ), t > 0 x \in (0,1), y \in Y, \hfill \\ D or N boundary conditions \hfill \\ \end{gathered} \right.$$ is considered, whereX is an appropriate subspace ofH ²(0, 1), (Y, ?) is a compact minimal flow. By analyzing the zero crossing number for certain invariant manifolds and the linearized spectrum, it is shown that a minimal setE?X × Y ofΠ, is uniquely ergodic if and only if (Y, ?) is uniquely ergodic andμ(Y ₀)=1, whereμ is the unique ergodic measure of (Y, ?),Y ₀={ity∈Y} Card(E∩P ^?1(y))=1},P:X × Y → Y is the natural projection (it was proved in an authors' earlier paper thatY ₀ is a residual subset ofY). Moreover, if (E, ?) is uniquely ergodic, then it is topologically conjugated to a subflow ofR ¹ ×Y. A consequence of the last result is the following: in the case that (Y, ?) is almost periodic,Π, is expected to have many purely almost automorphic motions which are not ergodic.     

Symmetry groups and the pseudo-Riemann spacetimes for mixed-hardening elastoplasticity

The constitutive postulations for mixed-hardening elastoplasticity are selected. Several homeomorphisms of irreversibility parameters are derived, among which X_a⁰ and X_c⁰ play respectively the roles of temporal components of the Minkowski and conformal spacetimes. An augmented vector X_a:=(YQ_a^t,YQ_a⁰)^t is constructed, whose governing equations in the plastic phase are found to be a linear system with a suitable rescaling proper time. The underlying structure of mixed-hardening elastoplasticity is a Minkowski spacetime $\text{M}{}^{\mathrm{n+1}}$ on which the proper orthochronous Lorentz group SO_o(n,1) left acts. Then, constructed is a Poincaré group ISO_o(n,1) on space X:=X_a+X_b, of which X_b reflects the kinematic hardening rule in the model. We also find that the space (Q_a^t,q₀^a) is a Robertson–Walker spacetime, which is conformal to X_a through a factor Y, and conformal to X_c:=(ρQ_a^t,ρQ_a⁰)^t through a factor ρ as given by ρ(q₀^a)=Y(q₀^a)/[1−2ρ₀Q_a⁰(0)+2ρ₀Y(q₀^a)Q_a⁰(q₀^a)]. In the conformal spacetime the internal symmetry is a conformal group.