Project/Area Number  09640221 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  Sophia University 
Principal Investigator 
OUCHI Sunao Sophia Univ.Fac.Science and Technology, professor, 理工学部, 教授 (00087082)

CoInvestigator(Kenkyūbuntansha) 
GOTO Satoshi Sophia Univ.Fac.Science and Technology, assistant, 理工学部, 助手 (00286759)
HIRATA Hitoshi Sophia Univ.Fac.Science and Technology, assistant, 理工学部, 助手 (20266076)
YOSHINO Kunio Sophia Univ.Fac.Science and Technology, lecturer, 理工学部, 講師 (60138378)
TAHARA Hidetoshi Sophia Univ.Fac.Science and Technology, professor, 理工学部, 教授 (60101028)
UCHIYAMA Koichi Sophia Univ.Fac.Science and Technology, professor, 理工学部, 教授 (20053689)
森本 光生 上智大学, 理工学部, 教授 (80053677)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Partial differential equations in the complex domain / Asymptotic expansion / singularity / 複素偏微分方程式 / 漸近展開 / 特異点 / 複素編微分方程式 
Research Abstract 
885352We study partial differential equation P(z, delta^<alpha>u) = 0 in the complex domain, where u(z) admits singularities on the complex hypersurface {z_0 = O}. The results are the following : 1. Let P(z, delta)u(z) = f(z) be a linear partial differential equation, where f(z) has also admits singularities on K.We show under some conditions on P(z, delta) that there is an exponent gamma > 0 such that if u(z) grows at most some exponential order near z0 0, that is, for any epsilon > 0, u(z) <less than or equal> C_<epsilon> exp(epsilonz_0^<gamma>) and f(z) has a Gevrey type asymptotic expansion f(z) = SIGMA^^+=__0fn(z^l) * 0 in a sectorial region, where fn(z^l) <less than or equal> AB^nGAMMA(n/gamma+1), then u(z) has also an asymptotic expansion like f(z) as z_0 tends to 0. 2. The existence of solutios of formal power series of z_0, whose coefficients have Gevrey type estimate. 3. The uniqueness of singular solutions in some class of functions for some nonlinear partial differential equations. We also study DaveyStewartson equation which is one of nonlinear Schrodinger type equations and obtain the global existence of the initial value problem with small initial data and decay estimates for this equation.
