Stability results for optimal systems

1969 ◽  
Vol 5 (22) ◽  
pp. 545 ◽  
Author(s):  
B.D.O. Anderson
Keyword(s):  
Stability Results

Epitaxial Growth in Dislocation-Free Strained Alloy Films

2002 ◽  
Vol 715 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Rashmi C. Desai
Keyword(s):  
Deposition Rate ◽  
Elastic Moduli ◽  
Composition Dependence ◽  
Critical Thickness ◽  
Lattice Misfit ◽  
Misfit Strain ◽  
Joint Stability ◽  
Alloy Films ◽  
The Stability ◽  
Stability Results

AbstractThe morphological and compositional instabilities in the heteroepitaxial strained alloy films have attracted intense interest from both experimentalists and theorists. To understand the mechanisms and properties for the generation of instabilities, we have developed a nonequilibrium, continuum model for the dislocation-free and coherent film systems. The early evolution processes of surface pro.les for both growing and postdeposition (non-growing) thin alloy films are studied through a linear stability analysis. We consider the coupling between top surface of the film and the underlying bulk, as well as the combination and interplay of different elastic effects. These e.ects are caused by filmsubstrate lattice misfit, composition dependence of film lattice constant (compositional stress), and composition dependence of both Young's and shear elastic moduli. The interplay of these factors as well as the growth temperature and deposition rate leads to rich and complicated stability results. For both the growing.lm and non-growing alloy free surface, we determine the stability conditions and diagrams for the system. These show the joint stability or instability for film morphology and compositional pro.les, as well as the asymmetry between tensile and compressive layers. The kinetic critical thickness for the onset of instability during.lm growth is also calculated, and its scaling behavior with respect to misfit strain and deposition rate determined. Our results have implications for real alloy growth systems such as SiGe and InGaAs, which agree with qualitative trends seen in recent experimental observations.

scholarly journals Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1431
Author(s):  
Bilal Basti ◽  
Nacereddine Hammami ◽  
Imadeddine Berrabah ◽  
Farid Nouioua ◽  
Rabah Djemiat ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Biological Models ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Single Form ◽  
Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

scholarly journals Existence and Ulam stability for implicit fractional q-difference equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Saïd Abbas ◽  
Mouffak Benchohra ◽  
Nadjet Laledj ◽  
Yong Zhou
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Difference Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Ulam Stability ◽  
Uniqueness Of Solutions ◽  
Stability Results ◽  
Rassias Stability

AbstractThis paper deals with some existence, uniqueness and Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference equations. Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, next we prove that our problem is generalized Ulam–Hyers–Rassias stable. Two illustrative examples are given in the last section.

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