共查询到20条相似文献,搜索用时 15 毫秒
1.
An approach is presented for computing the adjoint operator vector of a class of nonlinear (that is, partial-nonlinear) operator matrices by using the properties of conjugate operators to generalize a previous method proposed by the author. A unified theory is then given to solve a class of nonlinear (partial-nonlinear and including all linear) and non-homogeneous differential equations with a mathematical mechanization method. In other words, a transformation is constructed by homogenization and triangulation, which reduces the original system to a simpler diagonal system. Applications are given to solve some elasticity equations. 相似文献
2.
IntroductionFindingsufficientconditionsfornonoscillatoryofsolutionsisaproblemofgeneralinterestinthetheoryofordinaryanddelaydifferentialequations.Inthisworkweconsiderdds σ(s) dds r(s) dxds +q(s) dxdsβ +p(s)xα =f(s) ,(1)whereσ ,r,q,pandfarereal_valuedcontinuousfuncti… 相似文献
3.
郭艾 《应用数学和力学(英文版)》1999,20(6):683-689
1ProblemsandMainResultsInthispaper,westudythenonlinearvibrationsofinfiniterodswithviscoelasticity.Theconstitutionlawoftherods... 相似文献
4.
K. R. Raslan 《Nonlinear dynamics》2008,53(4):281-286
Exact solutions of some important nonlinear partial differential equations are obtained by using the first integral method.
The efficiency of the method is demonstrated by applying it for two selected equations. 相似文献
5.
INITIALBOUNDARYVALUEPROBLEMSFORACLASSOFNONLINEARINTEGRO-PARTIALDIFFERENTIALEQUATIONSCuiShang-bin(崔尚斌)(Dept.ofMath.,LanzhouUni... 相似文献
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7.
王培光 《应用数学和力学(英文版)》2000,21(5):585-590
IntroductionDuetotheaccurenceofagreatdealofmathematicmodellingsdescribedinpartialfunctionaldifferentialequationsintheapplicationfieldsofmechanicsandcontroltheory[1],greatinterestwasarousedastothestudiesonthepropertyofthesolutionsofthistypeofequations.G… 相似文献
8.
A class of time fractional partial differential equations is considered, which in- cludes a time fractional diffusion equation, a time fractional reaction-diffusion equation, a time fractional advection-diffusion equation, and their corresponding integer-order partial differential equations. The fundamental solutions to the Cauchy problem in a whole-space domain and the signaling problem in a half-space domain are obtained by using Fourier- Laplace transforms and their inverse transforms. The appropriate structures of the Green functions are provided. On the other hand, the solutions in the form of a series to the initial and boundary value problems in a bounded-space domain are derived by the sine- Laplace or cosine-Laplace transforms. Two examples are presented to show applications of the present technique. 相似文献
9.
This paper studies the necessary and sufficient condition of uniformly convergent difference scheme for the elliptic-parabolic partial differential equation with a small parameter.Communicated by Lin Zong-chi. 相似文献
10.
A methodology for investigating stationary and travelling waves with spatially localized envelopes is presented. The nonlinear governing partial differential equations considered possess a constant first integral of motion, and are separable in space and time when the small parameter of the problem is set to zero. To study stationary waves, a coordinate transformation on the governing nonlinear partial differential equation is imposed which eliminates the time dependence from the problem. An amplitude modulation function is then introduced to express the response of the system at an arbitrary point as a nonlinear function of a reference response. Analytic approximations to the amplitude modulation function are developed by expressing it in power series, and asymptotically solving sets of singular functional equations at the various orders of approximation. Travelling solutions may be computed from stationary ones, by imposing appropriate Lorentz transformations. As an application of the methodology, stationary and travelling breathers of a nonlinear partial differential equation are analytically computed. 相似文献
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12.
刘玉记 《应用数学和力学(英文版)》2002,23(3):355-362
IntroductionConsidertheglobalattractivityofthenonlineardelaydifferenceequationΔxn+anxn+f(n ,∑0s=-k qs,nxs+n) =0 (n=0 ,1 ,2 ,… ) . ( 1 )TheinitialvalueofEq .( 1 )isxs =φs (s=-k ,-k+ 1 ,… ,-1 ,0 ) . ( 2 )Inthesequel,wealwayssupposethatD1) an isanonnegativerealsequence ,0 ≤an <1andkisapositive… 相似文献
13.
This paper studies the application of the continuous sensitivity equation method (CSEM) for the Navier–Stokes equations in the particular case of shape parameters. Boundary conditions for shape parameters involve flow derivatives at the boundary. Thus, accurate flow gradients are critical to the success of the CSEM. A new approach is presented to extract accurate flow derivatives at the boundary. High order Taylor series expansions are used on layered patches in conjunction with a constrained least‐squares procedure to evaluate accurate first and second derivatives of the flow variables at the boundary, required for Dirichlet and Neumann sensitivity boundary conditions. The flow and sensitivity fields are solved using an adaptive finite‐element method. The proposed methodology is first verified on a problem with a closed form solution obtained by the Method of Manufactured Solutions. The ability of the proposed method to provide accurate sensitivity fields for realistic problems is then demonstrated. The flow and sensitivity fields for a NACA 0012 airfoil are used for fast evaluation of the nearby flow over an airfoil of different thickness (NACA 0015). Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
14.
金均 《应用数学和力学(英文版)》1996,17(4):387-392
RESEARCHOFTHEPERIODICSOLUTIONFORACLASSOF NONLINEARDIFFERENTIALEQUATIONSRESEARCHOFTHEPERIODICSOLUTIONFORACLASSOFNONLINEARDIFFE... 相似文献
15.
宋光兴 《应用数学和力学(英文版)》1996,17(11):1081-1085
EXISTENCETHEOREMSOFEXTREMALSOLUTIONSFORACLASSOFNONLINEARINTEGRO-DIFFERENTIALEQUATIONSSongGuangxing(宋光兴)(ReceivedMay4,1995;Com... 相似文献
16.
In this paper, existence and uniqueness of the generalized global solution and the classical global solution to the initial value problem for a class of fourth-order nonlinear wave equations are studied in the fractional order Sobolev space using the contraction mapping principle and the extension theorem. The sufficient conditions for the blow up of the solution to the initial value problem are given. 相似文献
17.
GLOBAL SOLUTION OF THE INVERSE PROBLEM FOR ACLASS OF NONLINEAR EVOLUTION EQUATIONSOF DISPERSIVE TYPE
IntroductionItiswell_knownthatpseudo_parabolicequationwithprincipalpartut -uxxthasbeenstudyingrecently ,becausethereexistswidephysicalbackgroundforthisclassofequations.[1 ]studiedthemulti_dimensioninverseproblemforthefollowingclassofnonlinearevolutionequ… 相似文献
18.
The inverse problem for a class of nonlinear evolution equations of dispersive type was reduced to Cauchy problem of nonlinear
evolution equation in an abstract space. By means of the semigroup method and equipping equivalent norm technique, the existence
and uniqueness theorem of global solution was obtained for this class of abstract evolution equations, and was applied to
the inverse problem discussed here. The existence and uniqueness theorem of global solution was given for this class of nonlinear
evolution equations of dispersive type. The results extend and generalize essentially the related results of the existence
and uniqueness of local solution presented by YUAN Zhong-xin.
Contributed by Chen Yu-shu
Foundation item: the National Natural Science Foundation of China (Significance 199990510); the National Key Basic Research Special Foundation
of China (G1998020316); Liuhui Center for Applied Mathematics, Nankai University & Tianjin University
Biography: Chen Fang-qi (1963-) 相似文献
19.
卢德渊 《应用数学和力学(英文版)》1995,16(12):1185-1200
INSTABILITYOFSOLUTIONFORACLASSOFTHETHIRDORDERNONLINEARDIFFERENTIALEQUATIONLuDeyuan卢德渊(ReceivedNov101994CommunicatedbyZhangShi... 相似文献
20.
The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution
of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution
were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application
of the method of boundary layer with multiple scales.
Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM
Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼) 相似文献