簡単な放物型偏微分方程式の特有初期値問題 : 古典的解法と関数解析(その2)

概要

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First of all, I showed the proof of the uniqueness and the existence of solution on the characteristic initial value problem of the parabolic patial differential equation, one was of strong solution of the classical analysis, and the other was of weak solution of the functional analysis. In general, the exsistence of weak solution does not always guarantee one of classical solution. Applying these theories to the fluid dynamics, I showed that the functional analysis was superior to the classical one to solving Rayleigh's, unsteady Stokes's and Oseen's flow problem. In the functional analysis, the governing equations of these problems were transformed into the evolution equations, and were solved by the semi group theory. The solutions by evolution equations were summarized systematically in this paragraph 3. I gave seven considerations in this paper, three one among these were on the evolution equations, another ones were on the fluid dynamics. From these considerations, I think it is very important to analize the partial differential equations with the semi group theory.
広島文化学園大学の論文
1999-07-31