摘要:

AbstractThis paper is concerned with boundary control of one‐dimensional vibrating media whose motion is governed by a wave equation with a 2n‐order spatial self‐adjoint and positive‐definite linear differential operator with respect to 2nboundary conditions. Control is applied to one of the boundary conditions and the control function is allowed to vary in the Sobolev spaceW 01,pforp∈[2, ∞] With the aid of Banach space theory of trigonometric moment problems, necessary and sufficient conditions for null‐controllability are derived and applied to vibrating strings and Euler beams.For vibrating strings also, null‐controllability byLp‐controls on the boundary is shown by a direct method which makes use of d'Alembert's solution formula fo

ISSN:0170-4214    

DOI:10.1002/mma.1670170202

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractThis paper is concerned with the question of necessary and sufficient conditions to find a vector fieldV∈ Γ(TM) solving the equation divV= Φ under inhomogeneous boundary conditionsV|∂M= Z|∂MwithZ∈ Γ (TM) An existence and regularity result is given for an arbitrary Riemannian manifold with boundary,M. The proof is based on the Hodge theory of differen

ISSN:0170-4214    

DOI:10.1002/mma.1670170203

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractFor the theory of boundary value problems in linear elasticity, it is of crucial importance that the space of vector‐valuedL2‐functions whose symmetrized Jacobians are square‐integrable should be compactly embedded inL2. For regions with the cone property this is usually achieved by combining Korn's inequalities and Rellich's selection theorem. We shall show that in a class of less regular regions Korn's second inequality fails whereas the desired compact embedding still holds

ISSN:0170-4214    

DOI:10.1002/mma.1670170204

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

摘要:

AbstractWe study the propagation of linear waves, generated by a compactly supported time‐harmonic force distribution, in an infinite string under the assumption that the material properties are p1‐periodic forx>aand p2‐periodic forx<−a. As has been pointed out in two preceding papers devoted to related configurations ([4], [5]), the combination of a time‐periodic force and a periodic spatial structure may lead to resonance phenomena. We show that the present configuration also permits resonances of orders t and t1/2for a discrete set of frequencies. The occurrence of resonances is closely related to the presence of non‐trivial solutions of the corresponding time‐independent homogeneous problem which satisfy certain asymptotic properties (‘s

ISSN:0170-4214    

DOI:10.1002/mma.1670170205

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670170201

出版商:John Wiley&Sons, Ltd    

年代:1994

数据来源: WILEY