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.
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 language | English |
|---|---|
| Pages (from-to) | 41-65 |
| Number of pages | 25 |
| Journal | Journal of Partial Differential Equations |
| Volume | 25 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Jan 2012 |
Keywords
- Linear systems of first-order PDEs; Classification; Canonical systems.