抄録
Offer Organization: Japan Society for the Promotion of Science, System Name: Grants-in-Aid for Scientific Research, Category: Grant-in-Aid for Scientific Research (S), Fund Type: -, Overall Grant Amount: - (direct: 65300000, indirect: 19590000)
We were working on the development and applications of the numerical verification methods for solutions of nonlinear partial differential equations, in particular, we succeeded in finding a new and very efficient verification principle for nonlinear evolutional problems. Also we extended and improved the existing verification methods for solutions of elliptic problems as well as we proved the effectiveness of the computer assisted proofs by applying our methods to resolve the actual nonlinear problems for which any theoretical approaches seem to be not useful to apply.