Optimal Control of a Quasilinear Parabolic Equation and its Time Discretization

Computing Optimal Control with a Quasilinear Parabolic Partial Differential Equation

This paper presents the numerical solution of a constrained optimal control problem (COCP) for quasilinear parabolic equations. The COCP is converted to unconstrained optimization problem (UOCP) by applying the exterior penalty function method. Necessary optimality conditions for the considered problem are established. The computing optimal controls are helped to identify the unknown coefficien...

A Quasilinear Parabolic Equation With Inhomogeneous Density and Absorption

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

Quenching Profile for a Quasilinear Parabolic Equation

where 00, Z>0, and uq(x) >0, Vx G [—1, Z]. Without loss of generality, we may assume that uq(x) is smooth and bounded above by 1 such that uo(±Z) = 1. Since uo(x) is positive, the local (in time) existence and uniqueness of a classical solution of the problem (1.1)—(1.3) are trivial (see [8]). Many results in quenching, such as single point quenching and profiles, are similar to those b...

Rational Approximation for a Quasilinear Parabolic Equation

Approximation theorems, analogous to known results for linear elliptic equations, are obtained for solutions of the heat equation. Via the Cole-Hopf transformation, this gives rise to approximation theorems for a nonlinear parabolic equation, Burgers’ equation.