Functiones et Approximatio Commentarii Mathematici

Formal solutions of Burgers type equations

Grzegorz Łysik

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 40, Number 1 (2009), 33-43.

Dates
First available in Project Euclid: 30 March 2009

Permanent link to this document
https://projecteuclid.org/euclid.facm/1238418796

Digital Object Identifier
doi:10.7169/facm/1238418796

Mathematical Reviews number (MathSciNet)
MR2527627

Zentralblatt MATH identifier
1182.35077

Subjects
Primary: 35C10: Series solutions
Secondary: 35A20: Analytic methods, singularities 35K55: Nonlinear parabolic equations 05A20: Combinatorial inequalities

Keywords
Burgers type equation formal solutions combinatorial estimates Gevrey estimates non-analyticity

Citation

Łysik, Grzegorz. Formal solutions of Burgers type equations. Funct. Approx. Comment. Math. 40 (2009), no. 1, 33--43. doi:10.7169/facm/1238418796. https://projecteuclid.org/euclid.facm/1238418796


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