TY - JOUR
T1 - Partial Differential Equations That Are Hard to Classify
AU - Howison , S. D.
AU - Lacey , A. A.
AU - Ockendon , J. R.
JO - Journal of Partial Differential Equations
VL - 1
SP - 41
EP - 65
PY - 2012
DA - 2012/03
SN - 25
DO - http://doi.org/10.4208/jpde.v25.n1.4
UR - https://global-sci.org/intro/article_detail/jpde/5174.html
KW - Linear systems of first-order PDEs
KW - classification
KW - canonical systems
AB - <p>Semi-linear n×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 sides of the equations. 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.</p>