共查询到17条相似文献,搜索用时 46 毫秒
1.
沈臻 《应用数学和力学(英文版)》2003,24(5):555-567
IntroductionForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1]- [4 ].Thepaper (Ⅰ )oftheauthordiscussedtheill_posednessoftheCauchyproblemswhichsatisfythesameconditionsoftheinitialvalueproblematthehypersurfacet=t( 0 ) +g(x) ,g(x) ≠constant,g(0 ) =0 R4,andgavetwodifferentformalsolutions[5 ].Italsogavetheformulasforcomputation .Inthepresentpaper,twokindsofillposednessoftheEulerequation… 相似文献
2.
The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed.
And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed
initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist
any unique solution.
Foundation item: the National Natural Science Foundation of China (19971054)
Biography: Shen Zhen (1977−) 相似文献
3.
沈臻 《应用数学和力学(英文版)》2003,24(5):545-554
1 IntroductionandSignsForthestudyofwellposednessontheinitialorboundaryproblemsabouttheEulerequations,therearemanyimportantresultsgivenbydifferentmethodsindifferentfunctionclasses[1- 3].Andthereislessdiscussiononitsillposedness[4 ,5 ].Inthedifferentialfunctionclasses,BaouondiandGoulaouicprovedthattheCauchyproblemonthecompactmanifoldofEulerequationshasuniquesolutionwellexpectaconstant[4 ].InthebooktitledSolutionsAnalytiquesdeQuelquesEquationsauxDerivesPartiellesenMecaniquedesFluides,thest… 相似文献
4.
Shen Zhen 《应用数学和力学(英文版)》2003,24(5):545-554
The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification
theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods
of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial
value problem on hyper plane {t=0} in R4, and explain that the problem has more than one solution.
Foundation item: the National Natural Science Foundation of China (19971054)
Biography: Shen Zhen (1977−) 相似文献
5.
The initial problem for second order linear evolution equation systems is discussed byusing the contraction semigroup theory.A kind of initial value problem for second order isalso discussed with variable coefficients for evolution equations by using the analyticalsemigroup theory,and is unified with the solutions of the initial value problem for this classof equations and those of first order temporally inhomogeneous evolution equations.This isan important class of equations in mathematical mechanics. 相似文献
6.
The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time. 相似文献
7.
Using the theory of coincidence degree, a class of higher order multi-point boundary value problem for ordinary differential equations are studied. Under the boundary conditions satisfying the resonance case, some new existence results are obtained by supposing some conditions to the nonlinear term and applying a priori estimates. 相似文献
8.
CAUCHY PROBLEM OF ONE TYPE OF ATMOSPHERE EVOLUTION EQUATIONS 总被引:1,自引:0,他引:1
One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, (i) the inertial force has no influence on the criterion of the well-posed Cauchy problem; (ii) the compressibility plays no role on the well-posed condition of the Cauchy problem of the viscid atmosphere equations, but changes the well-posed condition of the viscid atmosphere equations; (iii) this type of atmosphere evolution equations is ill-posed on the hyperplane t = 0 in spite of its compressibility and viscosity; (iv) the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed. 相似文献
9.
INITIALBOUNDARYVALUEPROBLEMSFORACLASSOFNONLINEARINTEGRO-PARTIALDIFFERENTIALEQUATIONSCuiShang-bin(崔尚斌)(Dept.ofMath.,LanzhouUni... 相似文献
10.
郑永树 《应用数学和力学(英文版)》1981,(5)
In this paper we discuss singular perturbations offirst boundary value problem for higher order ellipticequations of two parameter and obtain the asymptoticexpression for the formal solution containing two-parameter as well as the estimation of its remainderterm.These results are the extensions of(2)and(3). 相似文献
11.
A systematic study was made on the topological nature of the system of non-static rotating fluid. Several initial (boundary) value problems and their well-posedness were discussed. 相似文献
12.
13.
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
14.
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
15.
In this paper,using a fixed point principle and existence principle given in[1],westudy the boundary value problems for second order differential equations.Some newexistence results are obtained. 相似文献
16.
邵孝湟 《应用数学和力学(英文版)》1991,12(10):1001-1008
In this paper,using the differentiability of the solution with respect to the initial value and the parameter,we present a method which,different from Liapunov’s direct method.will determine the stability of the non-stationary solution of the initial value problem when the non-stationary solution remains unknown. 相似文献
17.
Hu Haichang 《Acta Mechanica Sinica》1992,8(2):127-135
A boundary integral representation of plane biharmonic function is established rigorously by the method of unanalytical continuation
in the present paper. In this representation there are two boundary functions and four constants which bear a one to one correspondence
to biharmonic functions. Therefore the set of boundary integral equations with indirect unknowns based on this representation
is equivalent to the original differential equation formulation. 相似文献