On the solution of the viscous Burgers' equation with nonlinear viscosity
2004 (English)Report (Other academic)
The viscous Burgers' equation with nonlinear viscosity is considered. The equation is written as a quasilinear parabolic equation in divergence form, and existence of a weak solution is shown. The proof is based on Galerkin approximations which converges in a suitable Banach space. Finally, the Cole-Hopf transformation is used to derive an analytical solution in the case when the viscosity is constant. This solution turns out to be very ill-conditioned for numerical evaluations. The solution can be rewritten with the Poisson summation formula. Comparisons to a finite difference solution are done.
Place, publisher, year, edition, pages
Linköping: Linköpings universitet , 2004. , 18 p.
LiTH-MAT-R, ISSN 0348-2960
IdentifiersURN: urn:nbn:se:liu:diva-22770ISRN: LITH-MAT-R-2004-07Local ID: 2097OAI: oai:DiVA.org:liu-22770DiVA: diva2:243083