Geodesic
On Exact Solutions of a Sobolev Equation
Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 807-822

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A nonlinear Sobolev-type equation that can be used to describe nonstationary processes in the semiconductor medium is studied. A number of families of exact solutions of this equation that can be expressed in terms of elementary functions and quadratures is obtained; some of these families contain arbitrary sufficiently smooth functions of one argument. The qualitative behavior of the resulting solutions is analyzed.
Keywords: Sobolev space, nonlinear differential equation, algebraic and differential nonlinearities, blow-up of a solution. 
@article{MZM_2017_101_6_a1,
     author = {A. I. Aristov},
     title = {On {Exact} {Solutions} of a {Sobolev} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {807--822},
     publisher = {mathdoc},
     volume = {101},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a1/}
}
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A. I. Aristov. On Exact Solutions of a Sobolev Equation. Matematičeskie zametki, Tome 101 (2017) no. 6, pp. 807-822. http://geodesic.mathdoc.fr/item/MZM_2017_101_6_a1/