Solution of continuous nonlinear PDEs through order completion / Michael B. Oberguggenberger, Elemér E. Rosinger.

By:

Oberguggenberger, Michael B

Contributor(s):

Series: North-Holland mathematics studies ; 181.1994Description: 1 online resource (xvi, 432 pages) : illustrationsContent type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9780444820358
0444820353
9780080872926
0080872921
128198471X
9781281984715

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Genre/Form:

Electronic books.

Additional physical formats: Print version:: Solution of continuous nonlinear PDEs through order completion.LOC classification:

QA372 .O33 1994eb

Online resources:

Click here to access online

Contents:

pt. 1. General existence of solutions theory -- pt. 2. Applications to specific classes of nonlinear and linear PDEs -- pt. 3. Group invariance of global generalized solutions of nonlinear PDEs.

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.

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eBooks

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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 (pages 421-428) and index.

Print version record.

pt. 1. General existence of solutions theory -- pt. 2. Applications to specific classes of nonlinear and linear PDEs -- pt. 3. Group invariance of global generalized solutions of nonlinear PDEs.

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