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Monotone increasing solutions of the Painlevé 1 equation y″ = y2+x and their role in the stability of the plasma-sheath transition

Published online by Cambridge University Press:  12 December 2002

M. SLEMROD
M. SLEMROD
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA email: [email protected]
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Abstract

This paper proves the existence and uniqueness of a monotone increasing solution of the Painlevé 1 equation y″ = y2+x. The monotonicity of solution is then exploited to show stability of the plasma-sheath transition in a weakly ionizing plasma.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 13 , Issue 6 , December 2002 , pp. 663 - 680
Copyright
2002 Cambridge University Press

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