We study the behavior of oscillatory solutions to convection-diffusion problems, subject to initial and forcing data with modulated multi-scale oscillations. We determine the weak W-l,OO-limit of the solutions when the small scales of the modulations tend to zero and quantify the weak convergence rate. Moreover, in case the solution operator of the equation is compact, this weak convergence is translated into a strong one. Examples include nonlinear conservation laws and equations with nonlinear degenerate diffusion.
|Original language||American English|
|Number of pages||9|
|Journal||Hokkaido University technical report series in mathematics|
|State||Published - 1 Jan 1996|
|Event||NONLINEAR WAVES Proceedings of the Fourth MSJ International Research Institute Vol II - Hokkaido Prefecture, Sapporo, Japan|
Duration: 10 Jul 1995 → 21 Jul 1995