6月3日(木) 15:30 -- 17:00 西田 詩 (鹿児島大学)
``Finite Difference Scheme on a Banach Scale''
＜研究発表要旨＞
We consider a partial differential equation
\frac{\partial u}{\partial t}
= \sum_{j=1}^{J} A_{j}(t, x, u) \frac{\partial u}{\partial x_{j}}
+ B(t, x, u) in t > 0, |x| < \rho ,
where x is a J-dimensional complex vector and u is a N-dimensional complex
valued function, with the initial value
u(0, x) = \varphi(x), |x|<\rho_{0}.
We assume analyticity of coefficients and initial value, and we apply the
finite difference method to this problem. In this research, we show ,under
certain assumption, that the approximate solution uniformly converges to the
exact one in some compact domain, and we deal with it in a Banach scale.
We also give a brief report concerning about the initial value problem of
the Cauchy-Riemann equation.