On a Backward-Forward Parabolic Equation and Its Regularization

A forward-backward-forward differential equation and its asymptotic properties

In this paper, we approach the problem of finding the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space via an implicit forward-backward-forward dynamical system with nonconstant relaxation parameters and stepsizes of the resolvents. Besides proving existence and uniqueness of strong global solutions for the differential equati...

A backward–forward regularization of the Perona–Malik equation

Article history: Received 18 February 2011 Revised 28 October 2011 Available online 6 December 2011

Fourier regularization for a backward heat equation ✩

In this paper a simple and convenient new regularization method for solving backward heat equation— Fourier regularization method is given. Meanwhile, some quite sharp error estimates between the approximate solution and exact solution are provided. A numerical example also shows that the method works effectively. © 2006 Elsevier Inc. All rights reserved.

Homogenization of forward-backward parabolic equations

We study the homogenization of the equation R(εx) ∂uε ∂t −∆uε = f , where R is a periodic function which may vanish or change sign, with appropriate initial/final conditions. The main tool is a compactness result for sequences of functions which have bounded norms in the spaces associated to the problems.

A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient