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van der Walt, Jan Harm

The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives. (English) Zbl 1154.35328

Acta Appl. Math. 103, No. 1, 1-17 (2008).
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.

Cited in 9 Documents

MSC:

35G20 Nonlinear higher-order PDEs
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
06B30 Topological lattices
46E05 Lattices of continuous, differentiable or analytic functions

Keywords:

convergence space; uniform convergence structures
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\textit{J. H. van der Walt}, Acta Appl. Math. 103, No. 1, 1--17 (2008; Zbl 1154.35328)
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