We consider the Cauchy problem for a general inhomogeneous linear partial differential equation with constant coefficients in two complex variables. We obtain necessary and sufficient conditions for the multisummability of formal solutions in terms of analytic continuation properties and growth estimates of some functions connected with the inhomogeneity. The results are presented in the general framework of 1/p-fractional equations.
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Michalik, S. Multisummability of formal solutions of inhomogeneous linear partial differential equations with constant coefficients. J Dyn Control Syst 18, 103–133 (2012). https://doi.org/10.1007/s10883-012-9136-5
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DOI: https://doi.org/10.1007/s10883-012-9136-5
Key words and phrases
- Fractional linear PDEs with constant coefficients
- formal power series
- Borel summability
- multisummability
- Duhamel principle