Abstract
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.
Citation
Grzegorz Łysik. "Formal solutions of Burgers type equations." Funct. Approx. Comment. Math. 40 (1) 33 - 43, March 2009. https://doi.org/10.7169/facm/1238418796
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