摘要:

AbstractThe paper deals with the stationary Boltzmann equation in a bounded convex domain Ω. The boundary ∂Ω is assumed to be a piecewise algebraic variety of theC2‐class that fulfils Liapunov's conditions. On the boundary we impose the so‐called Maxwell boundary conditions, that is a convex combination of specular and diffusive reflections. The non‐linear Boltzmann equation is considered with additional volume and boundary source terms and it has been proved that for sufficiently small sources the problem possesses a unique solution in a properly chosen subspace ofC(Ω × ℝ3). The proof is a refined version of the proof delivered by Guiraud for purely diffusi

ISSN:0170-4214    

DOI:10.1002/mma.1670150602

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractWe prove the existence of guided waves propagating with a velocity strictly larger than theS(shear) wave velocity at infinity in the case of unbounded elastic media invariant under translation in one space direction and asymptotically homogeneous at infinity.These waves correspond to the existence of eigenvalues embedded in the essential spectrum of the self‐adjoint elastic propagato

ISSN:0170-4214    

DOI:10.1002/mma.1670150603

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractRegularized inner products,r(s,e1,e2,) of the distorted plane waves fór the plasma wave equationuu− Δu+qu= 0 are introduced for potentials with compact support. The regularized inner product may be represented in terms of the far‐field pattern. The use of the WKB approximation shows that the behaviour ofrase2→ −e1is closely related to the Radon transform ofq. This observation indicates the possibility of finding the Radon transform ofqin terms ofr(s,e1,e2) and then of recoveringqby means of the inverse Radon

ISSN:0170-4214    

DOI:10.1002/mma.1670150604

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractWe investigate an unsteady viscous flow problem where ‘good’ boundary conditions are available on part of the boundary only. This problem appears when the flow phenomena one is interested in are concentrated on part of the flow region and, for reasons of computational economy, are numerically computed in this subregion only. Assuming that outside of the subregion the flow is not subjected to any acceleration forces, we develop an (abstract) combined finite‐element/boundary element scheme to compute the flow approximately. This scheme leads to a proof of the existence of a weak solution of the corresponding Navier–Stokes problem

ISSN:0170-4214    

DOI:10.1002/mma.1670150605

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

摘要:

AbstractRecent monographs and research articles have demonstrated that the highly complicated bifurcation structure, which usually arises in the presence of high symmetries, can often be systematically reduced with group theoretic concepts. Equivariant branching theorems and bifurcation subgroups have been the principle tools in this direction of investigation. The generalizations that we give allow the discussions of new classes of problems and the weakening of the usual hypotheses of absolute irreducibility of the group representation or of the appropriate subspaces. These extensions are illustrated in the case of a class of planar semilinear elliptic partial differential equations, which are usually treated as model problems in fluid mechanics and chemical reactions.

ISSN:0170-4214    

DOI:10.1002/mma.1670150606

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670150601

出版商:John Wiley&Sons, Ltd    

年代:1992

数据来源: WILEY