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Zbl 1154.35328
van der Walt, Jan Harm
The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives. (English)
[J] Acta Appl. Math. 103, No. 1, 1-17 (2008). ISSN 0167-8019; ISSN 1572-9036/e

Summary: By setting up appropriate uniform convergence structures, we are able to reformulate the order completion method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs. As an application, we obtain existence and uniqueness results for the solutions of arbitrary continuous, nonlinear PDEs.

MSC 2000:: *35G20 General theory of nonlinear higher-order PDE
54A20 Convergence in general topology
06B30 Topological lattices
46E05 Lattices of functions defined by smoothness properties

Keywords: convergence space; uniform convergence structures

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Zentralblatt MATH Berlin [Germany]