摘要:

AbstractConsider the partial differential equation:wt+bw+a· ∇w=gin ℝn× [0,T] (x1<0) and if the functiona1is positive, then, in the left half‐space, the solution w is anO(ν) for small Vis

ISSN:0170-4214    

DOI:10.1002/mma.1670130602

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractHyperthermia is an aid to standard cancer therapy. The aim is to heat up a tumour region inside the patient's body with the help of microwave radiation. The microwayes are generated by some suitable antenna array. Here we investigate the control properties of such antenna configurations and determine their resolution capabilities. We will define the hyperthermia operator, which can produce every field of any antenna array up to any degree of accuracy. We shall see that this operator is compact and we are able to compute a singular system under general assumptions explicitly. This, together with a detailed knowledge of the decay of the singular values, constitutes the tools with which we treat the previously stated problems. We examine the propagation of microwave radiation in homogeneous media and then carry over the results obtained to the case of inhomogeneous media.

ISSN:0170-4214    

DOI:10.1002/mma.1670130603

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractWe present a global existence theorem for solutions ofutt− ∂iaik(x)∂ku+ ut= ƒ(t,x,u,ut, ∇u, ∇ut, ∇2u),u(t= 0) =u0,u  t(=0)=u1,u(t, x),t⪖ 0,xϵΩ.Ω equals ℝ3or Ω is an exterior domain in ℝ3with smoothly bounded star‐shaped complement. In the latter case the boundary conditionu|∂Ω= 0 will be studied. The main theorem is obtained for small data (u0,u1) under certain conditions on the coefficientsaik.TheLp‐Lqdecay rates of solutions of the linearized problem, based on a previously introduced generalized eigenfunction expansion ansatz, are used to derive

ISSN:0170-4214    

DOI:10.1002/mma.1670130604

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

摘要:

AbstractIn this paper we consider initial‐boundary value problems for systems with a small parameter ϵ. The problems are mixed hyperbolic–parabolic when ϵ>0 and hyperbolic when ϵ = 0. Often the solution can be expanded asymptotically in ϵ and to first approximation it consists of the solution of the corresponding hyperbolic problem and a boundary layer part. We prove sufficient conditions for the expansion to exist and give estimates of the remainder. We also examine how the boundary conditions should be choosen to avoidO(1) boundary

ISSN:0170-4214    

DOI:10.1002/mma.1670130605

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY

ISSN:0170-4214    

DOI:10.1002/mma.1670130601

出版商:John Wiley&Sons, Ltd    

年代:1990

数据来源: WILEY