Partial Differential Equations That Are Hard to Classify

Partial Differential Equations That Are Hard to Classify

Year:    2012

Author:    S. D. Howison, A. A. LACEY, J. R. Ockendon

Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jpde.v25.n1.4

Journal of Partial Differential Equations, Vol. 25 (2012), Iss. 1 : pp. 41–65

Published online:    2012-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Linear systems of first-order PDEs

Author Details

S. D. Howison

A. A. LACEY

J. R. Ockendon