We study formal power series solutions to the initial value problem for the Burgers type equation $\partial_t u-\Delta u = X\big(f(u)\big)$ with polynomial nonlinearity $f$ and a vector field $X$, and prove that they belong to the formal Gevrey class $G^2$. Next we give counterexamples showing that the solution, in general, is not analytic in time at $t=0$. We also prove the existence of non-constant globally analytic solutions.
Publié le : 2009-03-15
Classification:
Burgers type equation,
formal solutions,
combinatorial estimates,
Gevrey estimates,
non-analyticity,
35C10,
35A20,
35K55,
05A20
@article{1238418796,
author = {\L ysik, Grzegorz},
title = {Formal solutions of Burgers type equations},
journal = {Funct. Approx. Comment. Math.},
volume = {40},
number = {1},
year = {2009},
pages = { 33-43},
language = {en},
url = {http://dml.mathdoc.fr/item/1238418796}
}
Łysik, Grzegorz. Formal solutions of Burgers type equations. Funct. Approx. Comment. Math., Tome 40 (2009) no. 1, pp. 33-43. http://gdmltest.u-ga.fr/item/1238418796/