摘要:

AbstractWe consider the equation (−1)m∇m(p∇mu) + ∂ t2u= ƒ in ℝn× [0, ∞] for arbitrary positive integersmandnand under the assumptionsp−1, ƒ ϵC 0∞andp>0. Under the additional assumption that the differential operator (−1)m∇m(p∇mu) has no eigenvalues we derive an asymptotic expansion foru(x,t) ast→ including all terms up to ordero(1). In particular, we show that for 2m≥nterms of the orderstα, logt,

ISSN:0170-4214    

DOI:10.1002/mma.1670180102

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractTwo non‐classical model interface problems for piecewise homogeneous anisotropic bodies are studied. In both problems on the contact surface jumps of the normal components of displacement and stress vectors are given. In addition, in the first problem (Problem H) the tangent components of the displacement vectors are given from both sides of the contact surface, while in the second one (Problem G) the tangent components of the stress vectors are prescribed on the same surface. The existence and uniqueness theorems are proved by means of the boundary integral equation method, and representations of solutions by single layer potentials are established. In the investigation the general approach of regularization of the first kind of integral equations is worked out for the case of two‐dimensional closed smooth manifolds. An equivalent global regularizer operator is constructed explicitly in the form of a singular integro‐differential ope

ISSN:0170-4214    

DOI:10.1002/mma.1670180103

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractUnder a generalized Sommerfeld radiation condition, we proved the uniqueness and existence of the direct obstacle scattering problem of time‐harmonic acoustic waves in a stratified medium [8]. In this paper, we study the asymptotic behaviour of the scattered waves and prove three reciprocity relations among the free‐wave far‐field patterns and the guided‐wave far‐field pattern vectors corresponding to incident distorted plane waves and normal mode waves. Then we prove conditions under which a set of far‐field patterns is complete in a Hilbert space based on the reciprocity relation. These properties are important in investigating the inverse obstacle scatteri

ISSN:0170-4214    

DOI:10.1002/mma.1670180104

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

摘要:

AbstractThe problem of robot motion planning in an environment with obstacles can often be reduced to the study of connectivity of the robot's free configuration space. In turn, space connectivity can be analysed via the correspondingconnectivity graph. For two‐degree‐of‐freedom robots, the free configuration space presents atwo‐dimensional(2D)surface—a compact subspace of a 2D orientable compact manifold. This paper addresses the following abstract problem: given a compact 2D surface bounded by simple closed curves and lying in an orientable 2D manifold (a sphere, a torus, etc.) and given two points in the subspace, suggest a systematic way of defining the connectivity graph in the subspace, based on its topological properties. The use of space topology results in powerful, from the robotics standpoint, provable algorithms capable of on‐line motion planning in an environment with unknown obstacles of arbitrary shapes. This makes the method distinct from other techniques, which require complete information, algebraic representation of space geometry, and off‐lin

ISSN:0170-4214    

DOI:10.1002/mma.1670180105

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670180101

出版商:John Wiley&Sons, Ltd    

年代:1995

数据来源: WILEY