Abstract
The stability of the conical stationary solutions of the Kuramoto–Sivashinsky equation $u_t + \Delta ^2 u + \Delta u + |\nabla u|^2 = c^2 $ in one and two space dimensions is studied. It is shown that these solutions are unstable in the whole space. Next the problem is studied in the one-dimensional (1D) case in a bounded interval $|x| \leq l$ and in the 2D case in a disc $0 \leq r < l$ with natural boundary conditions. It is proved that for a large slope c the above stationary solutions are stable. In the 1D case part of the proof is computer assisted.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
