Robust Fuzzy H∞ Estimator-Based Stabilization Design for Nonlinear Parabolic Partial Differential Systems with Different Boundary Conditions

2021 ◽  
pp. 343-373
Author(s):  
Bor-Sen Chen
Keyword(s):  
Boundary Conditions ◽  
Partial Differential ◽  
Differential Systems ◽  
Different Boundary Conditions ◽  
Nonlinear Parabolic

scholarly journals Analysis of Different Boundary Conditions on Homogeneous One-Dimensional Heat Equation

2021 ◽  
Vol 7 (1) ◽  
pp. 15-21
Author(s):  
Norazlina Subani ◽  
Muhammad Aniq Qayyum Mohamad Sukry ◽  
Muhammad Arif Hannan ◽  
Faizzuddin Jamaluddin ◽  
Ahmad Danial Hidayatullah Badrolhisam
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Initial Value ◽  
Partial Differential ◽  
Different Boundary Conditions ◽  
One Dimensional ◽  
Profile Changes ◽  
The Right

Partial differential equations involve results of unknown functions when there are multiple independent variables. There is a need for analytical solutions to ensure partial differential equations could be solved accurately. Thus, these partial differential equations could be solved using the right initial and boundaries conditions. In this light, boundary conditions depend on the general solution; the partial differential equations should present particular solutions when paired with varied boundary conditions. This study analysed the use of variable separation to provide an analytical solution of the homogeneous, one-dimensional heat equation. This study is applied to varied boundary conditions to examine the flow attributes of the heat equation. The solution is verified through different boundary conditions: Dirichlet, Neumann, and mixed-insulated boundary conditions. the initial value was kept constant despite the varied boundary conditions. There are two significant findings in this study. First, the temperature profile changes are influenced by the boundary conditions, and that the boundary conditions are dependent on the heat equation’s flow attributes.

The homogenization of elliptic partial differential systems on rugous domains with variable boundary conditions

2013 ◽  
Vol 143 (2) ◽  
pp. 303-335 ◽  
Author(s):  
J. Casado-Díaz ◽  
M. Luna-Laynez ◽  
F. J. Suárez-Grau
Keyword(s):  
Boundary Conditions ◽  
Asymptotic Behaviour ◽  
Elliptic Problems ◽  
Elliptic Systems ◽  
Partial Differential ◽  
Differential Systems ◽  
Variable Boundary ◽  
Variable Boundary Conditions

This paper is devoted to studying the asymptotic behaviour of a sequence of elliptic systems posed in a sequence of rough domains Ωn. The solutions un are assumed to satisfy un(x) ϵ Vn(x), where Vn(x) is a vectorial space depending on $\smash{x\in\bar\varOmega_n}$. This enables one to consider several types of boundary conditions posed in variable sets of the boundary. For some choices of the vectorial spaces Vn(x), our study provides, in particular, some classical results for the homogenization of Dirichlet elliptic problems in varying domains.

scholarly journals Oscillation criteria for high order delay partial differential equations

1998 ◽  
Vol 11 (2) ◽  
pp. 193-208 ◽  
Author(s):  
Xinzhi Liu ◽  
Xilin Fu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
High Order ◽  
Differential Inequalities ◽  
Partial Differential ◽  
Oscillation Criteria ◽  
Different Boundary Conditions ◽  
Delay Differential ◽  
Delay Partial Differential Equations

This paper studies a class of high order delay partial differential equations. Employing high order delay differential inequalities, several oscillation criteria are established for such equations subject to two different boundary conditions. Two examples are also given.

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