http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Solution of continuous nonlinear PDEs through order completion
1 online resource (xvi, 432 pages) : illustrations
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.
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.
Michael B. Oberguggenberger, Elemér E. Rosinger.
Includes bibliographical references (pages 421-428) and index.
Amsterdam ; New York : North-Holland, 1994
126118:126454 Elsevier Science & Technology