共查询到20条相似文献,搜索用时 15 毫秒
1.
陈松林 《应用数学和力学(英文版)》1996,17(11):1095-1100
SINGULARPERTURBATIONFORANONLINEARBOUNDARYVALUEPROBLEMOFFIRSTORDERSYSTEMChenSonglin(陈松林)(ReceivedApril8,1984;RevisedApril15,19... 相似文献
2.
This paper is taken up for the following difference equation problem(P,)(L,y)_k≡εy(k 1) a(k,ε)y(k) b(k,ε)y(k-1)=f(k,ε)(1≤k≤N-1),B_1y≡-y(0) c_1y(1)=a,B_2y≡-c_2y(N-1) y(N)=βwhereεis a small parameter,c_1,c_2,a,βconstants and a(k,ε),b(k,ε),f(k,ε)(1≤k≤N)functions of k andε.Firstly,the case with constant coefficients isconsidered.Secondly,a general method based on extended transformation is given tohandle(P.)where the coefficients may be variable and uniform asymptotic expansionsare obtained Finally,a numerical example is provided to illustrate the proposed method. 相似文献
3.
Bruno D. Lopes Paulo R. da Silva Marco A. Teixeira 《Journal of Dynamics and Differential Equations》2017,29(4):1519-1537
In this article we deal with non-smooth dynamical systems expressed by a piecewise first order implicit differential equations of the form where \(g_1,g_2,\varphi :U\rightarrow \mathbb {R}\) are smooth functions and \(U\subseteq \mathbb {R}^2\) is an open set. The main concern is to study sliding modes of such systems around some typical singularities. The novelty of our approach is that some singular perturbation problems of the form arise when the Sotomayor–Teixeira regularization is applied with \((x, y) \in U\) , \(\varepsilon \ge 0\), and f, g smooth in all variables.
相似文献
$$\begin{aligned} \dot{x}=1,\quad \left( \dot{y}\right) ^2=\left\{ \begin{array}{lll} g_1(x,y) \quad \text{ if }\quad \varphi (x,y)\ge 0 \\ g_2(x,y) \quad \text{ if }\quad \varphi (x,y)\le 0 \end{array},\right. \end{aligned}$$
$$\begin{aligned} \dot{x}= f(x,y,\varepsilon ) ,\quad (\varepsilon \dot{ y})^2=g ( x,y,\varepsilon ) \end{aligned}$$
4.
Singular perturbations of two-point boundary problems for systems of ordinary differential equations
W. A. Harris Jr. 《Archive for Rational Mechanics and Analysis》1960,5(1):212-225
Asymptotic solutions of linear systems of ordinary differential equations are employed to discuss the relationship of the solution of a certain “complete” boundary problem.
$$\begin{gathered} \left\{ \begin{gathered} {\text{ }}\frac{{d{\text{ }}x_1 }}{{d{\text{ }}t}} = A_{11} (t,\varepsilon ){\text{ }}x_1 (t,\varepsilon ){\text{ }} + \cdots + A_{1p} (t,\varepsilon ){\text{ }}x_p (t,\varepsilon ) \hfill \\ \varepsilon ^{h_2 } \frac{{d{\text{ }}x_2 }}{{d{\text{ }}t}} = A_{21} (t,\varepsilon ){\text{ }}x_1 (t,\varepsilon ){\text{ }} + \cdots + A_{2p} (t,\varepsilon ){\text{ }}x_p (t,\varepsilon ) \hfill \\ {\text{ }} \vdots {\text{ }} \vdots {\text{ }} \vdots \hfill \\ \varepsilon ^{h_p } \frac{{d{\text{ }}x_2 }}{{d{\text{ }}t}} = A_{p1} (t,\varepsilon ){\text{ }}x_1 (t,\varepsilon ){\text{ }} + \cdots + A_{pp} (t,\varepsilon ){\text{ }}x_p (t,\varepsilon ) \hfill \\ \end{gathered} \right\} \hfill \\ {\text{ }}R(\varepsilon ){\text{ }}x(a,{\text{ }}\varepsilon ){\text{ }} + {\text{ }}S(\varepsilon ){\text{ }}x(b,{\text{ }}\varepsilon ) = c(\varepsilon ){\text{ }} \hfill \\ \end{gathered}$$ 相似文献
5.
In this paper we study linear reaction–hyperbolic systems of the form , (i = 1, 2, ..., n) for x > 0, t > 0 coupled to a diffusion equation for p
0 = p
0(x, y, θ, t) with “near-equilibrium” initial and boundary data. This problem arises in a model of transport of neurofilaments in axons.
The matrix (k
ij
) is assumed to have a unique null vector with positive components summed to 1 and the v
j
are arbitrary velocities such that . We prove that as the solution converges to a traveling wave with velocity v and a spreading front, and that the convergence rate in the uniform norm is , for any small positive α. 相似文献
6.
In [1], a class of multiderivative block methods (MDBM) was studied for the numerical solutions of stiff ordinary differential
equations. This paper is aimed at solving the problem proposed in [1] that what conditions should be fulfilled for MDBMs in
order to guarantee the A-stabilities. The explicit expressions of the polynomials
and
in the stability functions
are given. Furthermore, we prove
. With the aid of symbolic computations and the expressions of diagonal Pade' approximations, we obtained the biggest block
size k of the A-stable MDBM for any given l (the order of the highest derivatives used in MDBM, l≥1) 相似文献
7.
Flaviano Battelli 《Journal of Dynamics and Differential Equations》1994,6(1):147-173
We consider singularly perturbed systems
, such that=f(, o, 0). o
m
, has a heteroclinic orbitu(t). We construct a bifurcation functionG(, ) such that the singular system has a heteroclinic orbit if and only ifG(, )=0 has a solution=(). We also apply this result to recover some theorems that have been proved using different approaches. 相似文献
8.
王培光 《应用数学和力学(英文版)》1999,20(6):698-704
IntroductionOwingtotheextensiveapplicationofneutralequations,moreandmorestudieshavebenmadeonthebehaviorofthesolutions[1,2].Fo... 相似文献
9.
Lucineide Balbino da Silva Marcelo Massayoshi Ueki Marcelo Farah Vitor Manuel Coelho Barroso João Manuel Luis Lopes Maia Rosario Elida Suman Bretas 《Rheologica Acta》2006,45(3):268-280
Blends of polyethylene terephthalate (PET) with a liquid crystalline polymer (LCP) and a compatibilizer were produced by twin
screw extrusion and injection molding. Transesterification and compatibilization studies were made in a torque rheometer.
The morphology of the injection-molded plaques was studied by scanning electron microscopy. The blends shear growth function
was measured in a cone and plate rheometer. The elongational growth function
was measured in a modified rotational rheometer. Transesterification was observed in the PET/LCP/compatibilizer 95/5/0 blend.
The injection-molded plaques displayed the usual “skin-core” morphology. All the blends were highly shear-thinning, even at
low shear rates; thus, a zero-shear viscosity could not be calculated. The compatibilized blend had the highest shear viscosity
of all the blends, confirming the strong PET/LCP interphase and the effectiveness of the compatibilizing agent. On the other
hand, the 90/10/0 blend had the lowest shear viscosity. All the blends showed strain softening behavior, similar to the PET.
The 90/10/0 blend had the highest elongational growth function, while the 95/5/0 had the lowest. The compatibilized blend
had an intermediate behavior between both blends. 相似文献
10.
We consider as in Parts I and II a family of linearly elastic shells of thickness 2?, all having the same middle surfaceS=?(?)?R 3, whereω?R 2 is a bounded and connected open set with a Lipschitz-continuous boundary, and? ∈ ?3 (?;R 3). The shells are clamped on a portion of their lateral face, whose middle line is?(γ 0), whereγ 0 is a portion of?ω withlength γ 0>0. For all?>0, let $\zeta _i^\varepsilon$ denote the covariant components of the displacement $u_i^\varepsilon g^{i,\varepsilon }$ of the points of the shell, obtained by solving the three-dimensional problem; let $\zeta _i^\varepsilon$ denote the covariant components of the displacement $\zeta _i^\varepsilon$ a i of the points of the middle surfaceS, obtained by solving the two-dimensional model ofW.T. Koiter, which consists in finding $$\zeta ^\varepsilon = \left( {\zeta _i^\varepsilon } \right) \in V_K (\omega ) = \left\{ {\eta = (\eta _\iota ) \in {\rm H}^1 (\omega ) \times H^1 (\omega ) \times H^2 (\omega ); \eta _i = \partial _v \eta _3 = 0 on \gamma _0 } \right\}$$ such that $$\begin{gathered} \varepsilon \mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \gamma _{\sigma \tau } (\zeta ^\varepsilon )\gamma _{\alpha \beta } (\eta )\sqrt a dy + \frac{{\varepsilon ^3 }}{3} \mathop \smallint \limits_\omega a^{\alpha \beta \sigma \tau } \rho _{\sigma \tau } (\zeta ^\varepsilon )\rho _{\alpha \beta } (\eta )\sqrt a dy \hfill \\ = \mathop \smallint \limits_\omega p^{i,\varepsilon } \eta _i \sqrt a dy for all \eta = (\eta _i ) \in V_K (\omega ), \hfill \\ \end{gathered}$$ where $a^{\alpha \beta \sigma \tau }$ are the components of the two-dimensional elasticity tensor ofS, $\gamma _{\alpha \beta }$ (η) and $\rho _{\alpha \beta }$ (η) are the components of the linearized change of metric and change of curvature tensors ofS, and $p^{i,\varepsilon }$ are the components of the resultant of the applied forces. Under the same assumptions as in Part I, we show that the fields $\frac{1}{{2_\varepsilon }}\smallint _{ - \varepsilon }^\varepsilon u_i^\varepsilon g^{i,\varepsilon } dx_3^\varepsilon$ and $\zeta _i^\varepsilon$ a i , both defined on the surfaceS, have the same principal part as? → 0, inH 1 (ω) for the tangential components, and inL 2(ω) for the normal component; under the same assumptions as in Part II, we show that the same fields again have the same principal part as? → 0, inH 1 (ω) for all their components. For “membrane” and “flexural” shells, the two-dimensional model ofW.T. Koiter is therefore justified. 相似文献
11.
In this paper we consider the equation
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12.
We study the global attractor of the non-autonomous 2D Navier–Stokes (N.–S.) system with singularly oscillating external force of the form . If the functions g
0(x, t) and g
1 (z, t) are translation bounded in the corresponding spaces, then it is known that the global attractor is bounded in the space H, however, its norm may be unbounded as since the magnitude of the external force is growing. Assuming that the function g
1 (z, t) has a divergence representation of the form where the functions (see Section 3), we prove that the global attractors of the N.–S. equations are uniformly bounded with respect to for all . We also consider the “limiting” 2D N.–S. system with external force g
0(x, t). We have found an estimate for the deviation of a solution of the original N.–S. system from a solution u
0(x, t) of the “limiting” N.–S. system with the same initial data. If the function g
1 (z, t) admits the divergence representation, the functions g
0(x, t) and g
1 (z, t) are translation compact in the corresponding spaces, and , then we prove that the global attractors converges to the global attractor of the “limiting” system as in the norm of H. In the last section, we present an estimate for the Hausdorff deviation of from of the form: in the case, when the global attractor is exponential (the Grashof number of the “limiting” 2D N.–S. system is small).
相似文献
13.
Two theorems concerning the existence of positive solutions for the singular equation
are presented. The results are obtained by using the nonlinear Leray-Schauder alternative and the lower-upper solution method. 相似文献
14.
Xinyu He 《Journal of Mathematical Fluid Mechanics》2007,9(3):398-410
Let
be the exterior of the closed unit ball. Consider the self-similar Euler system
15.
Anne-Laure Dalibard 《Archive for Rational Mechanics and Analysis》2007,185(3):515-543
We study the limit as ε → 0 of the solutions of the equation . This problem has already been addressed in a previous article in the case of well-prepared initial data, i.e. when the microscopic
profile of the solution is adapted to the medium at time t = 0. Here, we prove that when the initial data is not well prepared, there is an initial layer during which the solution
adapts itself to match the profile dictated by the environment. The typical size of the initial layer is of order ε. The proof
relies strongly on the parabolic form of the equation; in particular, no condition of nonlinearity on A is required. 相似文献
16.
Michael Winkler 《Journal of Dynamics and Differential Equations》2008,20(1):87-113
The paper deals with positive solutions of the initial-boundary value problem for with zero Dirichlet data in a smoothly bounded domain . Here is positive on (0,∞) with f(0) = 0, and λ1 is exactly the first Dirichlet eigenvalue of −Δ in Ω. In this setting, (*) may possess oscillating solutions in presence
of a sufficiently strong degeneracy. More precisely, writing , it is shown that if then there exist global classical solutions of (*) satisfying and . Under the additional structural assumption , s > 0, this result can be sharpened: If then (*) has a global solution with its ω-limit set being the ordered arc that consists of all nonnegative multiples of the
principal Laplacian eigenfunction. On the other hand, under the above additional assumption the opposite condition ensures that all solutions of (*) will stabilize to a single equilibrium.
相似文献
17.
18.
Carlos Fuentes Michel Vauclin Jean-Yves Parlange Randel Haverkamp 《Transport in Porous Media》1996,23(1):31-36
We show that for a fractal soil the soil-water conductivity, K, is given by $$\frac{K}{{K_\varepsilon }} = (\Theta /\varepsilon )^{2D/3 + 2/(3 - D)}$$ where $K_\varepsilon$ is the saturated conductivity, θ the water content, ? its saturated value and D is the fractal dimension obtained from reinterpreting Millington and Quirk's equation for practical values of the porosity ?, as $$D = 2 + 3\frac{{\varepsilon ^{4/3} + (1 - \varepsilon )^{2/3} - 1}}{{2\varepsilon ^{4/3} \ln ,{\text{ }}\varepsilon ^{ - 1} + (1 - \varepsilon )^{2/3} \ln (1 - \varepsilon )^{ - 1} }}$$ . 相似文献
19.
The paper gives a solution of the random differential equation with random coefficient, that is
, where K (t) is a random process and is a damp coefficient, it is a little parameter. 相似文献
20.
李永昆 《应用数学和力学(英文版)》1999,20(5):579-584
IntroductionAtpresent,thereareonlyafewpapers[1~3]havingbenpublishedontheglobalexistenceofperiodicsolutionsforneutraldelaypopu... 相似文献
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