Solution of continuous nonlinear PDEs through order completion
著者
書誌事項
Solution of continuous nonlinear PDEs through order completion
（North-Holland mathematics studies, 181）
North-Holland, 1994
大学図書館所蔵 件 / 全38件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 421-428) and index
内容説明・目次
内容説明
This work inaugurates a new and general solution method for arbitrary continuous nonlinear PDEs. The solution method is based on Dedekind order completion of usual spaces of smooth functions defined on domains in Euclidean spaces. However, the nonlinear PDEs dealt with need not satisfy any kind of monotonicity properties. Moreover, the solution method is completely type independent. In other words, it does not assume anything about the nonlinear PDEs, except for the continuity of their left hand term, which includes the unkown function. Furthermore the right hand term of such nonlinear PDEs can in fact be given any discontinuous and measurable function.
目次
Part I: General Existence of Solutions Theory. 1. Introduction. 2. Approximation of Solutions of Continuous Nonlinear PDEs. 3. Spaces of Generalized Functions. 4. Extending T(x,D) to the Order Completion of Spaces of Smooth Functions. 5. Existence of Generalized Solutions. 6. A Few First Examples. 7. Generalized Solutions as Measurable Functions. Part II: Applications to Specific Classes of Linear and Nonlinear PDEs. 8. The Cauchy Problem for Nonlinear First Order Systems. 9. An Abstract Existence Result. 10. PDEs with Sufficiently Many Smooth Solutions. 11. Nonlinear Systems with Measures as Initial Data. 12. Solution of PDEs and the Completion of Uniform Spaces. 13. Partial Orders Compatible with a Nonlinear Partial Differential Operator. 14. Miscellaneous Results. Part III: Group Invariance of Global Generalized Solutions of Nonlinear PDEs. 15. Introduction. 16. Group Invariance of Global Generalized Solutions of Nonlinear PDEs Obtained Through the Algebraic Method. 17. Group Invariance of Generalized Solutions Obtained Through the Algebraic Method: An Alternative Approach. 18. Group Invariance of Global Generalized Solutions Obtained Through the Order Completion Method. Appendix. References. Index.
「Nielsen BookData」 より
