摘要:

AbstractWe prove existence and uniqueness theorems for weak solutions of equations describing stationary isothermic motion of a mixture of two viscous incompressible fluids with asymmetric stress tensor, in a bounded subset of ℝ3. The model of the flow we consider here assumes that some of coefficients characterizing isotropic properties of the fluid equal zer

ISSN:0170-4214    

DOI:10.1002/mma.1670171102

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe article studies the stability of rectilinear equilibrium shapes of a non‐linear elastic thin rod (column or Timoshenko's beam), the ends of which are pressed. Stability is studied by means of the Lyapunov direct method with respect to certain integral characteristics of the type of norms in Sobolev spaces. To obtain equations of motion, a model suggested in [16] is used. Furta [6]solved the problem of stability for all values of the parameter except bifurcational ones. When values of the system's parameter become bifurcational, the study of stability is more complicated already in a finite‐dimensional case. To solve a problem like that, one often has to use a procedure of solving the singularities described in [1], for example. In this paper a change of variables is made which, in fact, is the first step of the procedure mentioned. To prove instability, we use a Chetaev function which can be considered as an infinite‐dimensional analogue of functions suggested in [14, 9]. The article also investigates a linear problem on the stability of adjacent shapes of equilibrium when the parameter has supercritical values (post‐bu

ISSN:0170-4214    

DOI:10.1002/mma.1670171103

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractBoundary‐transmission problems for two‐dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a Sobolev space setting. The first problem of a quadrant with Dirichlet condition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by the same medium. Unique solvability can also be shown in the case of two different media up to exceptional cases of wave numbers, while the Fredholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one‐medium case, but the two‐media case turns out to be more complicated and the equivalent system of boundary pseudodifferential equations cannot be completely analysed by this re

ISSN:0170-4214    

DOI:10.1002/mma.1670171104

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThe dynamic thermoelastic impact of two rods is modelled by a coupled system of two quasivariational inequalities and two equalities that reflect a bilateral contact condition and a radiation condition for the temperatures. The existence of a weak solution is established using a penalization method that employs Galerkin approximations and a priori estimates.

ISSN:0170-4214    

DOI:10.1002/mma.1670171105

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670171101

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY