Parabolic Approximation to Variational Problems with Double Obstacles

Identification of obstacles for parabolic problems

Obstacle identification problems for parabolic equations and systems are considered. Unique continuation property plays an important role in the arguments. These arguments are based on the idea which was first used in the paper MR0847528 (87k:35248) of one of the authors earlier. The technique is applied to inverse problems for slightly compressible fluids and to inverse problems for the heat e...

Hyperbolic Relaxation Approximation to Nonlinear Parabolic Problems

A general idea for solving hyperbolic systems of conservation laws is to use a local relaxation approximation. The motivation is to have a simple discrete velocity kinetic type relaxation regularization which approximates the original system with a small dissipative correction. In this paper we extend the previous approach to systems of nonlinear parabolic equations. The corresponding relaxatio...

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...

A variational approach to double-porosity problems

In this paper we outline an approach by Γ-convergence to some problems related to ‘double-porosity’ homogenization. Various such models have been discussed in the mathematical literature, the first rigorous result for a linear double-porosity model having been obtained by Arbogast, Douglas and Hornung in [7]. The two-scale convergence approach to double-porosity problems was developed by Allair...

Variational Modeling of Parabolic Free Boundary Problems