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well-posedness
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Well-posedness of Two Mathematical Models for Alzheimer's Disease
, M.Sc. Thesis Sharif University of Technology ; Hesaaraki, Mahmoud (Supervisor)
Abstract
In season 1, we introduce a mathematical model of the in vivo progression of Alzheimer’s disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of Aβ -amyloid plaques based on the concentrations of Aβ oligomers, PrPC proteins, and the Aβ-×-PrPC complex, which are hypothesized to be responsible for synaptic tox- icity. We prove the well posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of β-amyloid is constant and also when it is described by a power law. In seson 2, We consider the existence and uniqueness of solutions of an initial-boundary...
Boundary stabilization of non-classical micro-scale beams
, Article Applied Mathematical Modelling ; Volume 37, Issue 20-21 , 2013 , Pages 8709-8724 ; 0307904X (ISSN) ; Najafi, A ; Salarieh, H ; Alasty, A ; Sharif University of Technology
2013
Abstract
In this paper, the problem of boundary stabilization of a vibrating non-classical micro-scale Euler-Bernoulli beam is considered. In non-classical micro-beams, the governing Partial Differential Equation (PDE) of motion is obtained based on the non-classical continuum mechanics which introduces material length scale parameters. In this research, linear boundary control laws are constructed to stabilize the free vibration of non-classical micro-beams which its governing PDE is derived based on the modified strain gradient theory as one of the most inclusive non-classical continuum theories. Well-posedness and asymptotic stabilization of the closed loop system are investigated for both cases...
On the well-posedness, equivalency, and low-complexity translation techniques of discrete-time hybrid automaton and piecewise affine systems
, Article Scientia Iranica ; Volume 29, Issue 2 D , 2022 , Pages 693-726 ; 10263098 (ISSN) ; Mokhtari, H ; Sharif University of Technology
Sharif University of Technology
2022
Abstract
The main contribution of this paper is to present the systematic and low-complexity translation techniques between a class of hybrid systems referred to as automaton-based Discrete-time Hybrid Automata (DHA) and piecewise affine (PWA) systems. As a starting point, the general modeling framework of the automaton-based DHA is represented, which models the controlled and uncontrolled switching phenomena between linear continuous dynamics including discrete and continuous states, inputs and outputs. The basic theoretical definitions on the state trajectories of the proposed DHA with forward and backward evolutions that yield forward and backward piecewise affine (FPWA and BPWA) systems are...