Adaptive output regulation for one‐dimensional parabolic equation with nonlocal term

2021 ◽  
Author(s):  
Weiwei Liu ◽  
Jun‐Min Wang
Keyword(s):  
Parabolic Equation ◽  
Output Regulation ◽  
Nonlocal Term ◽  
One Dimensional

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.

scholarly journals On a nonlinear singular one-dimensional parabolic equation and double Laplace decomposition method

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668653 ◽  
Author(s):  
Hassan Eltayeb Gadain ◽  
Imed Bachar
Keyword(s):  
Parabolic Equation ◽  
Laplace Transform ◽  
Convergence Analysis ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Adomian Decomposition ◽  
Laplace Decomposition Method

In this article, the double Laplace transform and Adomian decomposition method are used to solve the nonlinear singular one-dimensional parabolic equation. In addition, we studied the convergence analysis of our problem. Using two examples, our proposed method is illustrated and the obtained results are confirmed.

scholarly journals An elliptic–parabolic equation with a nonlocal term for the transient regime of a plasma in a Stellarator

2004 ◽  
Vol 198 (2) ◽  
pp. 321-355 ◽  
Author(s):  
J.I. Dı́az ◽  
M.B. Lerena ◽  
J.F. Padial ◽  
J.M. Rakotoson
Keyword(s):  
Parabolic Equation ◽  
Transient Regime ◽  
Nonlocal Term
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