Browsing by Author "Abdulla, Ugur G."
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Existence of Solution to an Optimal Control Problem for the Heat Equation
Earl, CurtisConsider the nonhomogeneous heat equation with Neumann and Robin boundary conditions: (See Poster for the equations (1)(4)). The problem (1)(4) is well posed for sufficiently well behaved data, but what if some of the ... 
Identification of Parameters in Systems Biology
Poteau, Roby (201905)Systems Biology is an actively emerging interdisciplinary area between biology and applied mathematics, based on the idea of treating biological systems as a whole entity which is more than the sum of its interrelated ... 
Multidimensional KolmogorovPetrovsky test for the boundary regularity and irregularity of solutions to the heat equation
Abdulla, Ugur G. (2005)This paper establishes necessary and sufficient condition for the regularity of a characteristic top boundary point of an arbitrary open subset of ( ) for the diffusion (or heat) equation. The result implies asymptotic ... 
On the Classification of the Second Minimal Orbits of the Continuous Endomorphisms on the Real Line and Universality in Chaos
Iqbal, Naveed H (201704)This dissertation presents full classification of second minimal odd periodic orbits of a continuous endomorphisms on the real line. A (2k + 1)periodic orbit (k ≥ 3) is called second minimal for the map f, if 2k−1 is a ... 
On the Inverse Multiphase Stefan Problem
Cevallos, Bruno Giuseppe Poggi (201507)We consider inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, ... 
On the optimal control of the free boundary problems for the second order parabolic equations. I. wellposedness and convergence of the method of lines
Abdulla, Ugur G. (201305)We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fi xed boundary is missing and must be found along with the temperature and free boundary. We employ optimal ... 
On the Qualitative Theory of the Nonlinear Degenerate Second Order Parabolic Equations Modeling ReactionDiffusionConvection Processes
AalRkhais, Habeeb Abed (201805)We consider nonlinear second order degenerate or singular parabolic equation ut − a(um)xx + buβ + c(up)x = 0, a, m, β, p > 0, b, c ∈ R describing reactiondiffusionconvection processes arising in many areas of science and ... 
Optimal Control of Coefficients for the Second Order Parabolic Free Boundary Problems
Hagverdiyev, Ali (202005)Dissertation aims to analyze inverse Stefan type free boundary problem for the second order parabolic PDE with unknown parameters based on the additional information given in the form of the distribution of the solution ... 
Optimal Control of Multiphase Free Boundary Problems for Nonlinear Parabolic Equations
Cosgrove, Evan (202008)Dissertation research is on the optimal control of systems with distributed parameters described by singular nonlinear partial differential equations (PDE) modeling multiphase Stefan type second order parabolic free ... 
Optimal Control of the Second Order Elliptic Equations with Biomedical Applications
Seif, Saleheh (202005)Dissertation analyzes optimal control of systems with distributed parameters described by the general boundary value problems in a bounded Lipschitz domain for the linear second order uniformly elliptic partial differential ... 
Qualitative Analysis of the Nonlinear Double Degenerate Parabolic Equation of Turbulent Filtration with Absorption
Prinkey, Adam (201905)The goal of the dissertation is to pursue qualitative analysis of the mathematical model of turbulent polytropic filtration of a gas in a porous media with reaction or absorption described by the second order nonlinear ... 
ReactionDiffusion in Nonsmooth and Closed Domains
Abdulla, Ugur G. (20061130)We investigate the Dirichlet problem for the parabolic equation in a nonsmooth and closed domain possibly formed with irregular surfaces and having a characteristic vertex point. Existence, boundary regularity, uniqueness, ...