Exact Solutions of a Nonclassical Equation with a Nonlinearity under the Laplacian

We study a nonlinear partial differential equation that models processes occurring in a semiconductor medium. Six classes of exact solutions of this equation expressed via elementary and special functions are obtained. The qualitative behavior of these solutions is analyzed. We show that some of the...

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Veröffentlicht in:	Differential equations 2019-10, Vol.55 (10), p.1317-1327
1. Verfasser:	Aristov, A. I.
Format:	Artikel
Sprache:	eng
Schlagworte:	Difference and Functional Equations Differential equations Exact solutions Mathematics Mathematics and Statistics Nonlinear differential equations Nonlinearity Ordinary Differential Equations Partial Differential Equations Qualitative analysis
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We study a nonlinear partial differential equation that models processes occurring in a semiconductor medium. Six classes of exact solutions of this equation expressed via elementary and special functions are obtained. The qualitative behavior of these solutions is analyzed. We show that some of them are bounded and some of them “blow up” (become infinite in finite time).
ISSN:	0012-2661 1608-3083
DOI:	10.1134/S0012266119100070