On Hill’s Equation with a Discontinuous Coefficient
نویسنده
چکیده
where q(x) and r(x) are real valued and all have period a. Also q(x) is piecewise continuous, r ′′(x) is piecewise continuous in (0,b) and (b,a) where 0< b < a and r(x)≥ r0 (> 0). Those values of complex parameter λ, for which periodic or antiperiodic problem associated with (1.1) and the x-interval (0,a) has a nontrivial solution y(x,λ), are called eigenvalues. An equation giving the eigenvalues of the periodic or the antiperiodic problem can be found. For the purpose, after we use the Liouville transformation
منابع مشابه
A High Order Approximation of the Two Dimensional Acoustic Wave Equation with Discontinuous Coefficients
This paper concerns with the modeling and construction of a fifth order method for two dimensional acoustic wave equation in heterogenous media. The method is based on a standard discretization of the problem on smooth regions and a nonstandard method for nonsmooth regions. The construction of the nonstandard method is based on the special treatment of the interface using suitable jump conditio...
متن کاملValidating Hemoglobin Saturation and Dissolved Oxygen in Tumors using the OxyLab Probe and Photoacoustic Imaging
The goal of this experiment is to validate the relationship between hemoglobin saturation (SaO2) and partial pressure of dissolved oxygen (pO2) in breast tumors in mice using photoacoustic computed tomographic (PCT) imaging and OxyLite probe, respectively. In its simplest form, the relationship is described by the dissociation curve, or Hill’s equation, for hemoglobin, and is modeled as a sigmo...
متن کاملUniqueness and Hölder stability of discontinuous diffusion coefficients in three related inverse problems for the heat equation
We consider the heat equation ∂ty − div(c∇y) = H with a discontinuous coefficient in three connected situations. We give uniqueness and stability results for the diffusion coefficient c(·) in the main case from measurements of the solution on an arbitrary part of the boundary and at a fixed time in the whole spatial domain. The diffusion coefficient is assumed to be discontinuous across an unkn...
متن کاملCarleman estimates for the heat equation with discontinuous diffusion coefficients
We consider the heat equation with a diffusion coefficient that is discontinuous at an interface. We give global Carleman estimates for solutions of this equation, even if the jump of the coefficient across the interface has not a constant sign. AMS classification scheme numbers: 35K05, 35K55, 35R05, 35R30
متن کاملOn the band gap structure of Hill’s equation
We revisit the old problem of nding the stability and instability intervals of a secondorder elliptic equation on the real line with periodic coe cients (Hill’s equation). It is well known that the stability intervals correspond to the spectrum of the Bloch family of operators de ned on a single period. Here we propose a characterization of the instability intervals. We introduce a new family o...
متن کامل