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Volume 25, Issue 1
Partial Differential Equations That Are Hard to Classify

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

DOI: 10.4208/jpde.v25.n1.4

J. Part. Diff. Eq., 25 (2012), pp. 41-65.

Published online: 2012-03

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  • Abstract

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.

  • Keywords

Linear systems of first-order PDEs classification canonical systems

  • AMS Subject Headings

35A21, 35A30, 35E20, 35N05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

howison@maths.ox.ac.uk (S. D. Howison)

A.A.Lacey@hw.ac.uk (A. A. Lacey)

ock@maths.ox.ac.uk (J. R. Ockendon)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-25-41, author = {Howison , S. D.Lacey , A. A. and Ockendon , J. R.}, title = {Partial Differential Equations That Are Hard to Classify}, journal = {Journal of Partial Differential Equations}, year = {2012}, volume = {25}, number = {1}, pages = {41--65}, abstract = {

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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v25.n1.4}, url = {http://global-sci.org/intro/article_detail/jpde/5174.html} }
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 -

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.

Howison , S. D.Lacey , A. A. and Ockendon , J. R.. (2012). Partial Differential Equations That Are Hard to Classify. Journal of Partial Differential Equations. 25 (1). 41-65. doi:10.4208/jpde.v25.n1.4
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