Numerical solution to a non-linear parabolic boundary control problem

Dinh Nho Hao; Nguyen Trung Thanh; H. Sahli

doi:10.1142/9789812770493_0008

Numerical solution to a non-linear parabolic boundary control problem

Dinh Nho Hao
, Nguyen Trung Thanh
, H. Sahli

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

The so-called difference of convex functions algorithm and the continuation technique are applied to solving the nonlinear parabolic boundary control problem (formula Presented) where α > 0 is given and y(x, t) = y(x, t; u) is the solution to the non-linear parabolic problem y_t(x,t)=y_xx(x,t), 0<x<t<T, y(x,0)=y₀(x), 0<x<1, y_x(0,t)=0, y_x(1,t)=g(y(1,t)) + u(t), 0<t<T with {u ε L∞([0,T])|u_min(t) ≤ u(t) ≤ u_max(t), for a.e. t ε [0,T]}. Numerical examples are given to show the efficiency of the method.

Original language	American English
Title of host publication	Advances in Deterministic and Stochastic Analysis
Publisher	World Scientific Publishing Co.
Pages	115-130
Number of pages	16
ISBN (Electronic)	9789812770493
ISBN (Print)	9812705503, 9789812705501
DOIs	https://doi.org/10.1142/9789812770493_0008
State	Published - Jan 1 2007
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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abstract = "The so-called difference of convex functions algorithm and the continuation technique are applied to solving the nonlinear parabolic boundary control problem (formula Presented) where α > 0 is given and y(x, t) = y(x, t; u) is the solution to the non-linear parabolic problem yt(x,t)=yxx(x,t), 00(x), 0x(0,t)=0, yx(1,t)=g(y(1,t)) + u(t), 0min(t) ≤ u(t) ≤ umax(t), for a.e. t ε [0,T]\}. Numerical examples are given to show the efficiency of the method.",

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N2 - The so-called difference of convex functions algorithm and the continuation technique are applied to solving the nonlinear parabolic boundary control problem (formula Presented) where α > 0 is given and y(x, t) = y(x, t; u) is the solution to the non-linear parabolic problem yt(x,t)=yxx(x,t), 00(x), 0x(0,t)=0, yx(1,t)=g(y(1,t)) + u(t), 0min(t) ≤ u(t) ≤ umax(t), for a.e. t ε [0,T]}. Numerical examples are given to show the efficiency of the method.

AB - The so-called difference of convex functions algorithm and the continuation technique are applied to solving the nonlinear parabolic boundary control problem (formula Presented) where α > 0 is given and y(x, t) = y(x, t; u) is the solution to the non-linear parabolic problem yt(x,t)=yxx(x,t), 00(x), 0x(0,t)=0, yx(1,t)=g(y(1,t)) + u(t), 0min(t) ≤ u(t) ≤ umax(t), for a.e. t ε [0,T]}. Numerical examples are given to show the efficiency of the method.

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BT - Advances in Deterministic and Stochastic Analysis

PB - World Scientific Publishing Co.

ER -

Numerical solution to a non-linear parabolic boundary control problem

Abstract

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