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