Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof

@article{Cyranka2015ExistenceOG,
  title={Existence of globally attracting solutions for one-dimensional viscous Burgers equation with nonautonomous forcing - a computer assisted proof},
  author={Jacek Cyranka and Piotr Zgliczynski},
  journal={SIAM J. Applied Dynamical Systems},
  year={2015},
  volume={14},
  pages={787-821}
}
We prove the existence of globally attracting solutions of viscous Burgers’ equation with periodic boundary conditions on the interval for some particular choices of viscosity and non-autonomous forcing. The attracting solution is periodic if the forcing is periodic. The method is general and can be applied to other similar partial differential equations. The proof is computer assisted. 
Related Discussions
This paper has been referenced on Twitter 4 times. VIEW TWEETS

From This Paper

Figures, tables, and topics from this paper.

Explore Further: Topics Discussed in This Paper

References

Publications referenced by this paper.
Showing 1-10 of 19 references

Differential and integral inequalities approach to oscillator design for a class of bilinear systems

2013 International Symposium on Next-Generation Electronics • 2013
View 4 Excerpts
Highly Influenced

On the Forced Burgers Equation with Periodic Boundary Condition

H. R. Jauslin, H. O. Kreiss, J. Moser
Proceedings of Symposia in Pure Mathematics, Vol. 65 • 1999
View 3 Excerpts
Highly Influenced

A mathematical model illustrating the theory of turbulence

P. Zgliczyński Cyranka
Stability and Error Bounds in the Numerical Intgration of Ordinary Differential Equations • 2008

R

C. Foias, O. Manley, R. Rosa
Temam Navier-Stokes Equations and Turbulence, Encyclopedia of Mathematics and Its Applications, Vol. 84, Cambridge Univeristy Press • 2008
View 1 Excerpt

Trapping regions and an ODE-type proof of an existence and uniqueness for Navier-Stokes equations with periodic boundary conditions on the plane, Univ. Iag

P. Zgliczyński
Acta Math., • 2003

Similar Papers

Loading similar papers…