A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications

2005 ◽  
Vol 22 (1) ◽  
pp. 220-257 ◽  
Author(s):  
Mehdi Dehghan
Keyword(s):  
Parabolic Equation ◽  
Computational Study ◽  
One Dimensional ◽  
The One

scholarly journals Uniqueness and stability of solutions for a type of parabolic boundary value problem

1989 ◽  
Vol 12 (4) ◽  
pp. 735-739
Author(s):  
Enrique A. Gonzalez-Velasco
Keyword(s):  
Parabolic Equation ◽  
Boundary Value Problem ◽  
Nonnegative Solution ◽  
Boundary Value ◽  
Stability Of Solutions ◽  
General Boundary Conditions ◽  
Boundary Values ◽  
Parabolic Boundary ◽  
One Dimensional ◽  
The One

We consider a boundary value problem consisting of the one-dimensional parabolic equationgut=(hux)x+q, where g, h and q are functions of x, subject to some general boundary conditions. By developing a maximum principle for the boundary value problem, rather than the equation, we prove the uniqueness of a nonnegative solution that depends continuously on boundary values.

THE FINITE-DIFFERENCE METHOD OF ONE-DIMENSIONAL NONLINEAR SYSTEMS ANALYSIS

Fractals ◽  
2000 ◽  
Vol 08 (01) ◽  
pp. 49-65 ◽  
Author(s):  
A. YU. SHAHVERDIAN
Keyword(s):  
Time Series ◽  
Systems Analysis ◽  
Computational Study ◽  
Brain Activity ◽  
Logistic Map ◽  
Cantor Sets ◽  
Point Of View ◽  
One Dimensional ◽  
Time Flow ◽  
The One

The paper introduces one-dimensional analogy of Poincare "section" method. It reduces the one-dimensional nonlinear system orbit's study to consideration of some special conjugate orbit's "asymptotical" intersections with a thin arithmetical space of zero Lebesgue measure. The application of this approach to analysis of the logistic map orbits, earthquake time-series, and the sequences of fractional parts, is considered. Through computational study of these time-series, the existence of some Cantor sets, to which the conjugate orbits are attracted, is established. A fractal dynamical system, describing these different systems from a unified point of view, is introduced. The inner differential Cantorian structure of brain activity and time flow is discussed.

scholarly journals NULL CONTROLLABILITY OF DEGENERATE NONAUTONOMOUS PARABOLIC EQUATIONS

2019 ◽  
pp. 311
Author(s):  
Abbes Benaissa ◽  
Abdelatif Kainane Mezadek ◽  
Lahcen Maniar
Keyword(s):  
Parabolic Equation ◽  
Open Subset ◽  
Parabolic Equations ◽  
Diffusion Coefficients ◽  
Adjoint System ◽  
Null Controllability ◽  
Carleman Estimates ◽  
One Dimensional ◽  
Neumann Type ◽  
The One

In this paper we are interested in the study of the null controllability for the one dimensional degenerate non autonomous parabolic equation$$u_{t}-M(t)(a(x)u_{x})_{x}=h\chi_{\omega},\qquad  (x,t)\in Q=(0,1)\times(0,T),$$ where $\omega=(x_{1},x_{2})$ is asmall nonempty open subset in $(0,1)$, $h\in L^{2}(\omega\times(0,T))$, the diffusion coefficients $a(\cdot)$ isdegenerate at $x=0$ and $M(\cdot)$ is non degenerate on $[0,T]$. Also the boundary conditions are considered tobe Dirichlet or Neumann type related to the degeneracy rate of $a(\cdot)$. Under some conditions on the functions$a(\cdot)$ and $M(\cdot)$, we prove some global Carleman estimates which will yield the  observability inequalityof the associated adjoint system and equivalently the null controllability of our parabolic equation.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

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