ISSN:0010-3640    

DOI:10.1002/cpa.3160460202

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe inverse eigenvalue problem for a Sturm‐Liouville equation in impedance form with Dirichlet boundary conditions on a unit interval is considered. The solution of this nonlinear problem requires the investigation of a combined mapping from the logarithmic derivative of the impedance, assumed to be square integrable, to two sequences of spectral data. The first is the sequence of Dirichlet eigenvalues, shown to be locally bounded with square roots differing from the sequence of integral multiples of π by a square summable sequence. The second sequence has as first term the mean of the logarithmic derivative of the impedance. Each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint. It is shown that this is a locally bounded square summable sequence. The combined map is real analytic. The asymptotics and analyticity results follow from a modified Prüfer substitution. © 1993 John Wiley&Sons,

ISSN:0010-3640    

DOI:10.1002/cpa.3160460203

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe inverse eigenvalue problem for a Sturm‐Liouville equation in impedance form with Dirichlet boundary conditions on a unit interval is solved. The solution of this nonlinear problem requires the investigation of a combined map from the logarithmic derivative of the impedance, assumed to be square integrable, to two sequences of spectral data. The first is the sequence of Dirichlet eigenvalues, shown to be locally bounded with square roots differing from the sequence of integral multiples of π by a square summable sequence. The second sequence has as first term the mean of the logarithmic derivative of the impedance. Each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint. It is shown that this second sequence is a locally bounded square summable sequence.The combined map is a real analytic isomorphism. A uniqueness result follows from the asymptotics and analyticity shown in the first paper and properties of Riesz bases. The existence is shown by giving a closed form of the solution.It is also shown that the same map solves the inverse Sturm‐Liouville problem in impedance form with Neumann boundary conditions. © 1993 John Wiley&Sons

ISSN:0010-3640    

DOI:10.1002/cpa.3160460204

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460205

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe main result of this paper (which is completely new, apart from our previous and less general result proved in reference [9]) states that the nonlinear system of equations (1.11) (or, equivalently, (1.10)) that describes the motion of an inviscid, compressible (barotropic) fluid in a bounded domain Ω, gives rise to a strongly well‐posed problem (in the Hadamard classical sense) in spacesHk(Ω),k≧ 3; see Theorem 1.4 below. Roughly speaking, if (an, ϕn) → (a, ϕ) inHk×Hkand iffn→fin ℒ︁2(0,T;Hk), then (vn,gn) → (v, g) in

ISSN:0010-3640    

DOI:10.1002/cpa.3160460206

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460207

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

ISSN:0010-3640    

DOI:10.1002/cpa.3160460201

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY