Flow-Dependent Balance Conditions for Incremental Data Assimilation: Elliptic Operators

Analytic Solution for Hypersonic Flow Past a Slender Elliptic Cone Using Second-Order Perturbation Approximations

An approximate analytical solution is obtained for hypersonic flow past a slender elliptic cone using second-order perturbation techniques in spherical coordinate systems. The analysis is based on perturbations of hypersonic flow past a circular cone aligned with the free stream, the perturbations stemming from the small cross-section eccentricity. By means of hypersonic approximations for the ...

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

Inverse problem for Sturm-Liouville operators with a transmission and parameter dependent boundary conditions

In this manuscript, we consider the inverse problem for non self-adjoint Sturm--Liouville operator $-D^2+q$ with eigenparameter dependent boundary and discontinuity conditions inside a finite closed interval. We prove by defining a new Hilbert space and using spectral data of a kind, the potential function can be uniquely determined by a set of value of eigenfunctions at an interior point and p...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Pre- and Post- Processing in Data Assimilation

This paper provides an overview of the details of the data assimilation system implementation, at both pre and post-processing levels, which are, more often than not, mentioned in passing in data assimilation talks or articles. Data assimilation is the art of combining model and observations. It relies on a set of equations grounded on sound statistics. Some theoretical studies investigate ways...