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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2019, Number 8, Pages 13–20
DOI: https://doi.org/10.26907/0021-3446-2019-8-13-20 (Mi ivm9488) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Lambert function and exact solutions of nonlinear parabolic equations

A. A. Kosov, E. I. Semenov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, 134 Lermontov str., Irkutsk, 664033 Russia
Full-text PDF (365 kB) Citations (3)
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DOI: https://doi.org/10.26907/0021-3446-2019-8-13-20
Abstract: We consider the diffusion equations with degree type coefficient of diffusion and a nonlinear source. The main attention is paid to the construction of exact solutions expressed via the Lambert function. We prove a series of statements that determine the conditions for the source function that guarantee the existence of exact solutions of a certain type. We give examples of exact solutions of nonlinear diffusion equations (including those equations with polynomial and fractional-rational source functions) to illustrate the obtained results.
Keywords: equation of nonlinear diffusion, Lambert's function, exact solutions.
Funding agency Grant number
Russian Foundation for Basic Research 19-08-00746
Received: 18.06.2018
Revised: 18.06.2018
Accepted: 26.09.2018
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2019, Volume 63, Issue 8, Pages 10–16
DOI: https://doi.org/10.3103/S1066369X19080024
Bibliographic databases:
Document Type: Article
UDC: 517.958
Language: Russian
Citation: A. A. Kosov, E. I. Semenov, “Lambert function and exact solutions of nonlinear parabolic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 8, 13–20; Russian Math. (Iz. VUZ), 63:8 (2019), 10–16
Citation in format AMSBIB
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\paper Lambert function and exact solutions of nonlinear parabolic equations
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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\issue 8
\pages 13--20
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\crossref{https://doi.org/10.26907/0021-3446-2019-8-13-20}
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\jour Russian Math. (Iz. VUZ)
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\issue 8
\pages 10--16
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  • https://www.mathnet.ru/eng/ivm/y2019/i8/p13
    • This publication is cited in the following 3 articles:
    1. S. V. Solodusha, E. Yu. Grazhdantseva, “Testovoe polinomialnoe uravnenie Volterra I roda v zadache identifikatsii vkhodnykh signalov”, Tr. IMM UrO RAN, 27, no. 4, 2021, 161–174  mathnet  crossref  elib
    2. A. D. Polyanin, V. G. Sorokin, “Nonlinear pantograph-type diffusion PDEs: exact solutions and the principle of analogy”, Mathematics, 9:5 (2021), 511  crossref  isi  scopus
    3. A. A. Kosov, E. I. Semenov, “Exact solutions of the generalized richards equation with power-law nonlinearities”, Differ. Equ., 56:9 (2020), 1119–1129  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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