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References (4)
-
(2002)
Spravochnik po nelineinym uravneniyam matematicheskoi fiziki (Handbook of Nonlinear Equations of Mathematical Physics) -
M. Korpusov, D. Lukyanenko (2018)
Instantaneous blow-up versus local solvability for one problem of propagation of nonlinear waves in semiconductorsJournal of Mathematical Analysis and Applications, 459
-
(2010)
Metody nelineinoi matematicheskoi fiziki -
N.A. Kudryashov (2010)
Metody nelineinoi matematicheskoi fiziki (Methods of Nonlinear Mathematical Physics)
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Pleiades Publishing, Ltd.
- Subject
- Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/S0012266118090021
- Publisher site
- See Article on Publisher Site
Abstract
The equation ∂2 u/∂t∂x + u p ∂u/∂x = u q describing a nonstationary process in semiconductors, with parameters p and q that are a nonnegative integer and a positive integer, respectively, and satisfy p + q ≥ 2, is considered in the half-plane (x, t) ∈ ℝ × (0,∞). All in all, fourteen families of its exact solutions are constructed for various parameter values, and qualitative properties of these solutions are noted. One of these families is defined for all parameter values indicated above.
Journal
Differential Equations – Springer Journals
Published: Oct 13, 2018