摘要:

AbstractIn the framework of homogenization theory we study a mixture of an elastic solid and a viscous compressible fluid with periodic structure and its limit behaviour as the period tends to zero Existence, uniqueness and convergence theorems are given. The limit behaviour is viscoelastic.

ISSN:0170-4214    

DOI:10.1002/mma.1670020102

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThe paper gives a proof, valid for a large class of bounded domains, of the following compactness statements: LetGbe a bounded domain, β be a tensor‐valued function onGsatisfying certain restrictions, and let {n} be a sequence of vector‐valued functions onGwhere theL2‐norms of {n}, {curln}, and {div(βn)} are bounded, and where allneither satisfy xn= 0 or (βFn) = 0 at the boundary ∂GofG( = normal to ∂G): then {n} has aL2‐convergent subsequence. The first boundary condition is satisfied by electric fields, the second one by magnetic fields at a perfectly conducting boundary ∂Gif β is interpreted as electric dielectricity ϵ or as magnetic permeability μ, respectively.These compactness statements are essential for the application of abstract scattering theory to the boundary value problem for

ISSN:0170-4214    

DOI:10.1002/mma.1670020103

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractUsing some elementary generalisations of the Erdélyi‐Kober operators of fractional integration the solutions of some general integral equations are obtained in concise forms from which the solutions of several well known examples of the equations are easily fou

ISSN:0170-4214    

DOI:10.1002/mma.1670020104

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractQuasilinear transmission problems of both the elliptic and pseudoparabolic type with differential operators in divergence form simulating oxygen transport in capillary and tissue are investigated. Using recent methods of the theory of pseudomonotone operators and singular perturbations (elliptic regularization) the existence of weak solutions for both problems has been proven. Moreover, the weak solution of the elliptic problem proves to be a solution in the classical sense. Finally, at most one classical solution of a slightly modified pseudoparabolic problem exists.

ISSN:0170-4214    

DOI:10.1002/mma.1670020105

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractIn this paper we present new methods to solve the classical Dirichlet and Neumann problems for ΔU+k2U= 0. We prove that the solutions of this equation for a regionScontainingGrestricted toGare dense inL2(∂G). Introducing a basis in the space of solutions forSwe find a complete orthogonal system inL2(∂G) which can be used to solve the boundary value problems by means of approximation in the Hilbertspace norm. Regularity estimates lead to series expansions inG.The well‐known basis systems obtained by separation of variables thus may be used forevery regular region without the very special geometric restrictions.Another class of basis systems may be obtained in analogy to the Runge. theorems by considering types of singularity fun

ISSN:0170-4214    

DOI:10.1002/mma.1670020106

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThe problem of plasma confinement in a Tokomak machine has recently attracted considerable mathematical attention. In the present article, gradient bounds for the solution are obtained through the use of differential inequalities and the Hopf maximum principle. These estimates, which take slightly different forms in the plasma and vacuum regions, become exact in the one‐dimensional case. An estimate is also given for the distance from the boundary of the interior point where the maximum of the solution is attaine

ISSN:0170-4214    

DOI:10.1002/mma.1670020107

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractIt is well known that the free boundary of the one‐phase Stefan problem (1.1–5) depends continuously on the boundary data [1]. In this paper we prove that, in addition, the solution operator S which, to eachg. assigns the corresponding free boundary, is continuously Frechet differentiable and we give the defining formulas of the Frechet derivat

ISSN:0170-4214    

DOI:10.1002/mma.1670020108

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractThe qualitative behavior of the solutions of a reaction‐diffusion system arising in the theory of nuclear reactors is investigated by means of singular perturbation techniques, the small parameter ϵ representing the inverse of neutron velocity. At the lowest approximation for small ϵ the solutions exhibit oscillations about the unique strictly positive equilibrium, much as in the case of the associated lumped parameter system. A two‐times representation for solutions of small amplitudes is also

ISSN:0170-4214    

DOI:10.1002/mma.1670020109

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

摘要:

AbstractFor the Radon transform of functions with circular symmetry an inversion formula is proved in a new and elementary way. The inversion formula combined with Fourier theory is applied to Sommer‐feld's integral forH v1, yielding a representation of products which generalizes Nicholson's integral for |H v

ISSN:0170-4214    

DOI:10.1002/mma.1670020110

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670020101

出版商:John Wiley&Sons, Ltd    

年代:1980

数据来源: WILEY