09-97 Slawomir Michalik

Summability and fractional linear partial differential equations (326K, pdf) Jun 19, 09

Abstract , Paper (src), View paper (auto. generated pdf), Index of related papers

Abstract. We consider the Cauchy problem for the Kowalevskaya type fractional linear partial differential equations in two complex variables with constant coefficients. We show that solution is analytically continued in some directions with exponential growth if and only if the similar properties satisfy the Cauchy data. Applying this result we study the summability of formal power series solution of a Cauchy problem for general non-Kowalevskian linear partial differential equations in normal form with constant coefficients. We obtain the necessary and sufficient conditions for the Borel summability in terms of analytic continuation with an appropriate growth condition of the Cauchy data. Moreover, we show the similar characterisation of Borel summability in the case of non-Kowalevskian fractional equations.

Files: 09-97.src( 09-97.keywords , fractional.pdf.mm )