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2 Cyranka J.

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Computer Assisted Proofs in Dissipative Partial Differential Equations

Cyranka J.

Challenges of Modern Technology

2012

Vol. 3, no. 3

3--6

The goal of this paper is to present a brief survey of our research that has focused on studying the dynamics of dissipative partial differential equations by performing computer as sisted proofs. We provide a description of the main ideas behind the computer assisted proofs that we have performed, along with related topics. The emphasis is given to the case of the vis cous Burgers equation with constant forcing, for which the existence of globally attracting fixed points has been established. To achieve this goal, we used a combination of analytical results with computer assistance.

Rigorous Integration of Burgers Equation

Cyranka J.

Challenges of Modern Technology

2011

Vol. 2, no. 3

3--7

This paper presents techniques that allows to rigorously integrate dissipative partial differential equations. A full case study of an application to the Burgers equation on the line with periodic boundary conditions is presented.