Abstract – A new and accurate refractive index profile synthesis method for optical waveguides is demonstrated using the transmitted near electric field data. This method is based on an inverse transmission line technique. From Maxwell’s equations, we derive a transmission line equivalent circuit for the refractive index profile of a cylindrical dielectric waveguide. We demonstrate how to use t...

The Solow model is an economic model to describe economic growth. In this thesis we will provide an extension to this model by introducing a space dimension into the model and a production function that is non-concave. Furthermore, we will consider different kinds of technological progress. The resulting model is governed by a semilinear parabolic partial differential equation which describes t...

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We study an inverse parabolic problem of identifying two source terms in heat equation with dynamic boundary conditions from a final time overdetermination data. Using weak solution approach by Hasanov, the associated cost functional is analyzed, especially gradient formula proved and given adjoint problem. Next, existence uniqueness quasi-solution are also investigated. Finally, numerical reco...

Comparative analysis of inverse coefficient problems for parabolic equations. Part I: adjoint problem approach Alemdar Hasanov a b , Burhan Pektaş b & Arzu Erdem c a Institute of Mathematics, L.N. Gumilev Eurasian National University, 01008, Astana, Kazakhstan b Department of Mathematics and Computer Science, Izmir University, 35350 Izmir, Turkey c Department of Mathematics, Kocaeli University,...

We study the Cauchy problem for a parabolic system which is derived from a complexvalued heat equation with an inverse nonlinearity. First, we provide some criteria for the global existence of solutions. Then we consider the case when the initial data are asymptotically constants and obtain that, depending on the asymptotic limits, the solution quenches at space infinity or exists globally in t...

An inverse boundary determination problem for a parabolic model, arising in thermal imaging, is considered. The focus is on intelligently choosing an effective input heat flux, so as to maximize the practical effectiveness of an inversion algorithm. Three different methods, based on different interpretations of the term “effective”, are presented and analyzed, then demonstrated through numerica...

We revisit Smith’s frame of curvelets and discretize it making use of the USFFT as developed by Dutt and Roklin, and Beylkin. In the discretization, we directly approximate the underlying dyadic parabolic decomposition, its (rotational) symmetry, and approximate all the necessary decay estimates in phase space with arbitrary accuracy. Numerically, our transform is unitary. Moreover, if we apply...