Regularization of the backward-in-time Kuramoto–Sivashinsky equation

Regularization of the backward-in-time Kuramoto-Sivashinsky equation

We are interested in solution techniques for backward–in–time evolutionary PDE problems arising in fluid mechanics. In addition to their intrinsic interest, such techniques have applications in the recently proposed retrograde data assimilation. As our model system we consider the terminal value problem for the Kuramoto–Sivashinsky equation in a 1D periodic domain. Such backward problems are ty...

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.

A backward–forward regularization of the Perona–Malik equation

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

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

Controlling roughening processes in the stochastic KuramotoSivashinsky equation

We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into a linear stochastic and a nonlinear deterministic equation so that we can apply linear feedback control methods. Our control strateg...