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1.
In this paper, a class of nonlinear singularly perturbed initial boundary value problems for reaction diffusion equations with boundary perturbation are considered under suitable conditions. Firstly, by dint of the regular perturbation method, the outer solution of the original problem is obtained. Secondly, by using the stretched variable and the expansion theory of power series the initial layer of the solution is constructed. And then, by using the theory of differential inequalities, the asymptotic behavior of the solution for the initial boundary value problems is studied. Finally, using some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation are discussed.  相似文献   

2.
The problem of the boundary layer flow of power law non-Newtonian fluids with a novel boundary condition is studied.The existence and uniqueness of the solutions are examined,which are found to depend on the curvature of the solutions for different values of the power law index n.It is established with the aid of the Picard-Lindel¨of theorem that the nonlinear boundary value problem has a unique solution in the global domain for all values of the power law index n but with certain conditions on the curvature of the solutions.This is done after a suitable transformation of the dependent and independent variables.For 0 n 1,the solution has a positive curvature,while for n 1,the solution has a negative or zero curvature on some part of the global domain.Some solutions are presented graphically to illustrate the results and the behaviors of the solutions.  相似文献   

3.
An analytical solution is obtained for transient torsional vibration of a finite hollow cylinder with initial axial stress. The cylinder is subjected to dynamic shearing stress at the internal surface and is fixed at the external surface. The basic equations are presented and the solution is obtained by means of Fourier series expansion technique and the separation of variables method. The effects of the initial stress on the natural frequencies and transient torsional responses are presented and discussed.  相似文献   

4.
In this paper we consider singular perturbed phenomena of semilinear second order systems, under appropriate assumptions, the existence and asymptotic behavior as ε→0~+ of solution of vector boundary value problem are proved by constructing special invariant regions in which solutions display so-called boundary layer phenomena and angular layer phenomena.  相似文献   

5.
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations with boundary perturbation is considered. Under suitable conditions, first, the outer solution of the original problem was obtained. Secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer was constructed. Finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems was studied, and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation were discussed.  相似文献   

6.
In this paper we consider singular perturbed phenomena of semilinear second ordersystems, under appropriate assumptions, the existence and asymptotic behavior asε→0+ of solution of vector boundary value problem are proved by constructing specialinvariant regions in which solutions display so-called boundary layer phenomena andangular layer phenomena.  相似文献   

7.
A class of singularly perturbed boundary value problems for semilinear equations of fourth order with two parameters are considered. Under suitable conditions, using the method of lower and upper solutions, the existence and the asymptotic behavior of the solution to the boundary value problem are studied, In the present paper, the solution to the original singularly perturbed problem with two parameters has only one boundary layer.  相似文献   

8.
Self-similar behavior for the multicomponent coagulation system is investigated analytically in this paper. Asymptotic self-similar solutions for the constant kernel, sum kernel, and product kernel are achieved by introduction of different generating functions. In these solutions, two size-scale variables are introduced to characterize the asymptotic distribution of total mass and individual masses. The result of product kernel (gelling kernel) is consistent with the Vigli-Ziff conjecture to some extent. Furthermore, the steady-state solution with injection for the constant kernel is obtained, which is again the product of a normal distribution and the scaling solution for the single variable coagulation.  相似文献   

9.
The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation (ODE). Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.  相似文献   

10.
In this paper,the jumping problems of a circular thin plate with initial defletion arestudied by using the method of two variables proposed by Jiang Fu-ru and the methodof the normal perturbation(in this paper (1.1), (1.2)).We obtain Nth-order uniformly validasymptotic expansion of the solution of this problem ((1.66), (1.67)).When the initialdeflection vanishes the solution of a circular thinplate with initial deflection is reduced tothe solution of the problems of the nonlinear bending of a circular thin plate.If the initialdeflection is largish and the signs of the initial deflection with the intensity of the transverseload are opposite,when the intensity of the transverse load reaches a certain value,thecircular thin plate with initial deflection should produce the jumping phenomenon.  相似文献   

11.
A class of nonlinear nonlocal for singularly perturbed Robin initial boundary value problems for reaction diffusion equations is considered. Under suitable conditions, firstly, the outer solution of the original problem is obtained, secondly, using the stretched variable, the composing expansion method and the expanding theory of power series the initial layer is constructed, finally, using the theory of differential inequalities the asymptotic behavior of solution for the initial boundary value problems are studied and educing some relational inequalities the existence and uniqueness of solution for the original problem and the uniformly valid asymptotic estimation is discussed. Foundation items: the National Natural Science Foundation of China (10071048); the “Hunfred Talents Project” by Chinese Academy of Sciences Biography: Mo Jia-qi (1937−)  相似文献   

12.
We prove the asymptotic character of a solution of the Cauchy problem for a singularly perturbed linear system of differential equations with degenerate matrix of the coefficients of derivatives in the case where the limit matrix pencil is regular and has multiple “finite” and “infinite” elementary divisors. We establish conditions under which the constructed formal solutions are asymptotic expansions of the corresponding exact solutions. __________ Translated from Neliniini Kolyvannya, Vol. 10, No. 2, pp. 247–257, April–June, 2007.  相似文献   

13.
An initial-boundary value problem for shallow equation system consisting of water dynamics equations, silt transport equation, the equation of bottom topography change, and of some boundary and initial conditions is studied, the existence of its generalized solution and semidiscrete mixed finite element (MFE) solution was discussed, and the error estimates of the semidiscrete MFE solution was derived. The error estimates are optimal.  相似文献   

14.
By using “the method of modified two-variable”,“the method of mixing perturbation ”and introducing four small parameters, the problem of the nonlinear unsymmetrical bending for orthotropic rectangular thin plate with linear variable thickness is studied. And the uniformly valid asymptotic solution of Nth- order for ε1 and Mth- order for ε2 of the deflection functions and stress function are obtained.  相似文献   

15.
It is shown that the governing equation for the stream function of the Darcy free convection boundary layer flows past a vertical surface is invariant under arbitrary translations of the transverse coordinate y. The consequences of this basic symmetry property on the solutions corresponding to a prescribed surface temperature distribution T w (x) are investigated. It is found that starting with a “primary solution” which describes the temperature boundary layer on an impermeable surface, infinitely many “translated solutions” can be generated which form a continuous group, the “translation group” of the given primary solution. The elements of this group describe free convection boundary layer flows from permeable counterparts of the original surface with a transformed temperature distribution [(T)\tilde]w ( x ){\tilde {T}_w \left( x \right)}, when simultaneously a suitable lateral suction/injection of the fluid is applied. It turns out in this way that several exact solutions discovered during the latter few decades are in fact not basically new solutions, but translated counterparts of some formerly reported primary solutions. A few specific examples are discussed in detail.  相似文献   

16.
The derivation of an expression of the macroscopic stress tensor in terms of microscopic variables in systems of finite interacting particles is discussed from different points of view. It is shown that in volume averaging the introduction of a fictitious “interaction stress field”T I with special boundary conditions on the boundary of the averaging volume is needed. In ensemble averaging similar results are obtained by using a multipole expansion of the local stress and force fields. In the appropriate limiting cases, the obtained results are shown to be consistent with the results of kinetic theories of polymer solutions. Paper, presented at the First Conference of European Rheologists at Graz, April 14 – 16, 1982.  相似文献   

17.
We prove the asymptotic stability of two-state nonplanar Riemann solutions for a class of multidimensional hyperbolic systems of conservation laws when the initial data are perturbed and viscosity is added. The class considered here is those systems whose flux functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. In particular, we obtain the uniqueness of the self-similar L entropy solution of the two-state nonplanar Riemann problem. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in Lloc1 of the space of directions ξ = x/t. That is, the solution u(t, x) of the perturbed problem satisfies u(t, tξ)→R(ξ) as t→∞, in Lloc1(ℝn), where R(ξ) is the self-similar entropy solution of the corresponding two-state nonplanar Riemann problem.  相似文献   

18.
Fluid Mechanics of Tropical Cyclones   总被引:2,自引:0,他引:2  
Typhoons in the northwest Pacific and hurricanes in the northeast Atlantic are particular instances of a global phenomenon with frequently disastrous consequences known as the Tropical Cyclone (TC). This is an intense cyclone, generated over a tropical ocean with kinetic energy 1018 J or more, which extends over several hundred kilometres and yet is above all characterized by its calm central region: “the eye of the storm”. In a TC (not, of course, to be confused with such completely different phenomena as tornadoes) both the energy input and its dissipation mainly occur within that boundary layer between air and ocean which, at high TC wind speeds of 50–60 m/s, comprises essentially “a third fluid”: ocean spray. Afterwards, as a TC reaches land, disastrous effects of several different kinds may occur, and this paper outlines how fluid mechanics contributes towards worldwide struggles to reduce the human impact of TC disasters. Received 11 December 1996 and accepted 11 December 1996  相似文献   

19.
The flow in a laminar boundary layer for an arbitrary periodic main stream is considered at high frequencies when the fluid is incompressible. The analysis, incorporating length scales appropriate to the thin “Stokes” layer immediately adjacent to the surface and to the outer “Prandtl” boundary layer, involves expressing the dependent variables as mean parts plus superimposed periodic parts and expanding these in inverse powers of the frequency parameter in the two layers. Thus earlier approaches based on physical arguments are placed in the context of a systematic mathematical expansion scheme which is itself formulated for more general main stream velocities than hitherto. Expressions for skin friction and heat transfer are obtained and briefly discussed.  相似文献   

20.
THEPROBLEMSOFTHENONLINEARUNSYMMETRICAL.BENDINGFORCYLINDRICALLYORTHOTROPICCIRCULARPLATE(II)HuangJiayin(黄家寅);QinShengli(秦圣立);Xi...  相似文献   

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