Solution of continuous nonlinear PDEs through order completion [electronic resource] / Michael B. Oberguggenberger, Elem�er E. Rosinger.
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TextSeries: North-Holland mathematics studies ; 181.Publication details: Amsterdam ; New York : North-Holland, 1994. Description: 1 online resource (xvi, 432 p.) : illISBN: 9780444820358; 0444820353Subject(s): Differential equations, Nonlinear -- Numerical solutions | Parti�ele differentiaalvergelijkingen | Niet-lineaire vergelijkingen | Equations diff�erentielles non lin�eaires -- Solutions num�eriques | Differential equations, Nonlinear -- Numerical solutionsGenre/Form: Electronic books.Additional physical formats: Print version:: Solution of continuous nonlinear PDEs through order completion.DDC classification: 515/.353 LOC classification: QA372 | .O33 1994ebOnline resources: ScienceDirect | Volltext Summary: 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.
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.
Includes bibliographical references (p. 421-428) and index.
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