摘要:

AbstractThe procedure of Elliott and Janovsky is abstracted to a fairly general variational problem. As an application of the methodology a non‐isotropic Hele‐Shaw flow is trea

ISSN:0170-4214    

DOI:10.1002/mma.1670110401

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractWe discuss the stochastic structure of the Navier–Stokes flow in ℝ3and prove that it can be approximated by means of a finite‐dimensional stochastic process. Such a process reduces to an algorithm already discussed in Reference 4 for the Euler case, when the viscosity coefficient van

ISSN:0170-4214    

DOI:10.1002/mma.1670110402

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractUsing Ball's approach to non‐linear elasticity, and in particular his concept of polyconvexity, we treat a unilateral three‐dimensional contact problem for a hyperelastic body under volume and surface forces. Here the unilateral constraint is described by a sublinear function which can model the contact with a rigid convex cone. We obtain a solution to this generally non‐convex, semicoercive Signorinin problem as a limit of solutions of related energy minimization problems involving friction normal to the contact surface where the friction coefficient goes to infinity. Thus we extend an approximation result of Duvaut and Lions for linear‐elastic unilateral contact problems to finite deformations and to a class of non‐linear elastic materials including the material models of Ogden and of Mooney‐Rivlin for rubberlike materials.Moreover, the underlying penalty method is shown to be exact, that is a sufficiently large friction coefficient in the auxiliary energy minimization problems suffices to produce a solution of the original unilateral problem, provided a Lagrange multiplier to the unilateral constr

ISSN:0170-4214    

DOI:10.1002/mma.1670110403

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractWe present a semigroup analysis of the quantum Liouville equation, which models the temporal evolution of the (quasi) distribution of an electron ensemble under the action of a scalar potential. By employing the density matrix formulation of quantum physics we prove that the quantum Liouville operator generates a unitary group onL2if the corresponding Hamiltonian is essentially self‐adjoint.Also, we analyse the existence and non‐negativity of the particale density and prove that the solutions of the quantum Liouville equation converge to weak solutions of the classical Liouville equation as the Planck constant tends to zero (assuming that the potential is sufficiently smoo

ISSN:0170-4214    

DOI:10.1002/mma.1670110404

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non‐linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the piecewiseC1boundary. The boundary data are to be small in a weightedL∞

ISSN:0170-4214    

DOI:10.1002/mma.1670110405

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractStationary half‐space solutions of the linearized Boltzmann equation are studied by energy estimates methods. We extend the results of Bardos, Caflisch and Nicolaenko for a gas of hard spheres to a general potential. Asymptotic behaviour is obtained for hard as well as soft potentials and compared to the case of hard sphere

ISSN:0170-4214    

DOI:10.1002/mma.1670110406

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractA new solution of the two‐dimensional shallow‐water equations, using a finite element method is described. The formulation is based on the velocity and height variables and follows two steps. In the first step, the convective terms are solved by a characteristic method and in the second step the propagative and diffusion terms are taken into account. The close relation between the latter operator and a Stokes penalized problem is shown; an algorithm of Uzawa type is then used for its solution. Acceleration convergence is obtained by preconditioning, and new methods are presented, the quality of the convergence being shown on application to some sample tests. The overall method has revealed quite efficient and application to industrial cases is already plan

ISSN:0170-4214    

DOI:10.1002/mma.1670110407

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractConditions ensuring bifurcation from the infimum of the essential spectrum are given. The main result concerns non‐linear eigenvalue problems with variational structure in a Hilbert space. It extends previous results of a similar nature by admitting situations where the non‐linearity is not compact with respect to the graph norm of the linearization. The general result is applied to non‐linear elliptic equations

ISSN:0170-4214    

DOI:10.1002/mma.1670110408

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn this paper we construct canonical difference schemes of any order accuracy based on Padé approximation for Linear canonical systems with constant coefficients. For non‐linear Hamiltonian equations we will use an infinitesimally canonical transformation to construct canonical schemes of any order accura

ISSN:0170-4214    

DOI:10.1002/mma.1670110409

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY