Formal Solutions of Second Order Evolution Equations

  • Grzegorz Łysik

    Jan Kochanowski University, Kielce, Poland


We study the initial value problem for a second order evolution equation , where is a polynomial function in variables , , with coefficients analytic on a domain , and is analytic on . We construct a formal power series solution of the equation and prove that it satisfies Gevrey type estimates for and , where does not depend on . The proof is based on some combinatorial identities and estimates which may be of independent interest.

Cite this article

Grzegorz Łysik, Formal Solutions of Second Order Evolution Equations. Z. Anal. Anwend. 30 (2011), no. 1, pp. 95–104

DOI 10.4171/ZAA/1426