Partial differential equations that are hard to classify

S. D. Howison, A. A. Lacey, J. R. Ockendon

Research output: Contribution to journalArticle

Abstract

Semi-linear n x n systems of the form A u_x + B u_y = f can
generally be solved, at least locally, provided data are imposed on
non-characteristic curves. There are at most $n$ characteristic curves
and they are determined by
the coefficient matrices on the left-hand side of the equation.
We consider cases where such problems
become degenerate as a result of ambiguity associated with the
definition of characteristic curves.
In such cases, the existence of solutions
requires restrictions on the data and solutions might not be unique.
Original languageEnglish
Pages (from-to)41-65
Number of pages25
JournalJournal of Partial Differential Equations
Volume25
Issue number1
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • Linear systems of first-order PDEs; Classification; Canonical systems.

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