Existence of optimal controls for systems governed by parabolic partial differential equations with Cauchy boundary conditions

1980 ◽  
Vol 124 (1) ◽  
pp. 13-38 ◽  
Author(s):  
D. W. Reid ◽  
K. L. Teo
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Parabolic Partial Differential Equations ◽  
Optimal Controls ◽  
Partial Differential ◽  
Existence Of Optimal Controls

scholarly journals Existence theorems for optimal control of quasilinear parabolic partial differential equations

1979 ◽  
Vol 21 (1) ◽  
pp. 90-101 ◽  
Author(s):  
S. Nababan ◽  
E. S. Noussair
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Theorems ◽  
Parabolic Partial Differential Equations ◽  
Optimal Controls ◽  
Integral Functionals ◽  
Partial Differential ◽  
Lower Semi ◽  
Quasilinear Parabolic

AbstractThe question on existence of optimal controls for a system governed by quasilinear parabolic partial differential equations which is linear in the control variables is considered. It is shown that whenever the controls converge in the weak * topology of L∞, the corresponding solutions converge uniformly. Using this result and results on lower semi-continuity of integral functionals, existence theorems for optimal controls are proved.

An Accurate Jacobi Pseudospectral Algorithm for Parabolic Partial Differential Equations With Nonlocal Boundary Conditions

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
E. H. Doha ◽  
A. H. Bhrawy ◽  
M. A. Abdelkawy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Jacobi Polynomials ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Parabolic Partial Differential Equations ◽  
Partial Differential ◽  
Exponential Rate Of Convergence ◽  
Order Four

A new spectral Jacobi–Gauss–Lobatto collocation (J–GL–C) method is developed and analyzed to solve numerically parabolic partial differential equations (PPDEs) subject to initial and nonlocal boundary conditions. The method depends basically on the fact that an expansion in a series of Jacobi polynomials Jn(θ,ϑ)(x) is assumed, for the function and its space derivatives occurring in the partial differential equation (PDE), the expansion coefficients are then determined by reducing the PDE with its boundary conditions into a system of ordinary differential equations (SODEs) for these coefficients. This system may be solved numerically in a step-by-step manner by using implicit the Runge–Kutta (IRK) method of order four. The proposed method, in contrast to common finite-difference and finite-element methods, has the exponential rate of convergence for the spatial discretizations. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented.

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