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

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

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. and 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.

S. D. Howison, A. A. Lacey & J. R. Ockendon. (2019). 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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