Abstract
We construct formal power series solutions of nonlinear partial integro-differential equations with Fuchsian and irregular singularities at the origin of $$ \mathbb{C}^2 $$ for given initial conditions being formal power series. We give sufficient conditions under which there exist actual sectorial holomorphic solutions which are Gevrey asymptotic to the given formal series solutions for given 1-summable formal series initial conditions. A phenomenon of small divisors is observed for the appearance of singularities of the Borel transform of the constructed formal series due to the presence of the Fuchsian singularity. This property has an effect on the Gevrey asymptotic order for the constructed holomorphic solutions which becomes larger than the Gevrey order of the initial conditions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
