Browsing by Author "Abdulla, Ugur G."

Existence of Solution to an Optimal Control Problem for the Heat Equation

Earl, Curtis

Consider the non-homogeneous 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 (2019-05)

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 Kolmogorov-Petrovsky 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 (2017-04)

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 (2015-07)

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. well-posedness and convergence of the method of lines

Abdulla, Ugur G. (2013-05)

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 Reaction-Diffusion-Convection Processes

Aal-Rkhais, Habeeb Abed (2018-05)

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 reaction-diffusion-convection processes arising in many areas of science and ...