Solution of continuous nonlinear PDEs through order completion
Oberguggenberger, Michael B.
Solution of continuous nonlinear PDEs through order completion [electronic resource] / Michael B. Oberguggenberger, Elem�er E. Rosinger. - Amsterdam ; New York : North-Holland, 1994. - 1 online resource (xvi, 432 p.) : ill. - North-Holland mathematics studies ; 181 . - North-Holland mathematics studies ; 181. .
Includes bibliographical references (p. 421-428) and index.
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.
9780444820358 0444820353
126118:126454 Elsevier Science & Technology http://www.sciencedirect.com
Differential equations, Nonlinear--Numerical solutions.
Parti�ele differentiaalvergelijkingen.
Niet-lineaire vergelijkingen.
Equations diff�erentielles non lin�eaires--Solutions num�eriques.
Differential equations, Nonlinear--Numerical solutions.
Electronic books.
QA372 / .O33 1994eb
515/.353
Solution of continuous nonlinear PDEs through order completion [electronic resource] / Michael B. Oberguggenberger, Elem�er E. Rosinger. - Amsterdam ; New York : North-Holland, 1994. - 1 online resource (xvi, 432 p.) : ill. - North-Holland mathematics studies ; 181 . - North-Holland mathematics studies ; 181. .
Includes bibliographical references (p. 421-428) and index.
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.
9780444820358 0444820353
126118:126454 Elsevier Science & Technology http://www.sciencedirect.com
Differential equations, Nonlinear--Numerical solutions.
Parti�ele differentiaalvergelijkingen.
Niet-lineaire vergelijkingen.
Equations diff�erentielles non lin�eaires--Solutions num�eriques.
Differential equations, Nonlinear--Numerical solutions.
Electronic books.
QA372 / .O33 1994eb
515/.353
