We establish a Lipschitz stability estimate for the inverse problem consisting in the determination of the coe cient σ(t), appearing in a Dirichlet initial-boundary value problem for the parabolic equation ∂tu − ∆xu + σ(t)f(x)u = 0, from Neumann boundary data. We extend this result to the same inverse problem when the previous linear parabolic equation is changed to the semi-linear parabolic eq...

We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markov-modulated queues. We employ singular perturbation methods to study th...

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...

In this paper, a nonlinear inverse problem of parabolic type, is considered. By reducing this inverse problem to a system of Volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

An evacuated tube solar collector using therminol D-12 as heat transfer fluid coupled with parabolic trough is studied in this paper. An experimental set-up was constructed to study the performance of evacuated tube collector with therminol D-12 as heat transfer fluid. The parabolic trough is coupled with evacuated tube collector for better performance. In the traditional solar collectors water...

Rigidity and Stability for Isometry Groups in Hyperbolic 4-Space by Youngju Kim Advisor: Professor Ara Basmajian It is known that a geometrically finite Kleinian group is quasiconformally stable. We prove that this quasiconformal stability cannot be generalized in 4-dimensional hyperbolic space. This is due to the presence of screw parabolic isometries in dimension 4. These isometries are topol...

We prove that a parabolic subgroup P P contained in another P prime"> ′ encoding="application/x...

the release rate of potassium (k) from micaceous minerals plays a significant role in supplying k to plants. the objective of this study was to determine the most appropriate kinetic equation to describe potassium release from micaceous minerals as influenced by organic acids. muscovite and phlogopite were made to react with 0, 500, 2000 and 4000 ?m solutions of oxalic, citric and malic acids f...