V. M. Zhuravlev, “Exact solutions of the nonlinear diffusion equation $u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space”, TMF, 124:2 (2000), 265–278; Theoret. and Math. Phys., 124:2 (2000), 1082

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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 124, Number 2, Pages 265–278
DOI: https://doi.org/10.4213/tmf638 (Mi tmf638)

This article is cited in 7 scientific papers (total in 7 papers)

Exact solutions of the nonlinear diffusion equation

u_{t} = Δ \log u + λ u

$u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space

V. M. Zhuravlev

Ulyanovsk State University

Full-text PDF (215 kB) Citations (7)

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DOI: https://doi.org/10.4213/tmf638

Abstract: Investigating exact solutions of the nonlinear diffusion equation, which arises in wave problems in hydrodynamics and heat transfer processes, we find new classes of solutions of this equation in a two-dimensional coordinate space and demonstrate a special superposition principle that allows constructing complex multimode solutions from the simplest two- and three-mode solutions.

Received: 11.01.2000

English version:
Theoretical and Mathematical Physics, 2000, Volume 124, Issue 2, Pages 1082–1093
DOI: https://doi.org/10.1007/BF02551079

Bibliographic databases:

Language: Russian

Citation: V. M. Zhuravlev, “Exact solutions of the nonlinear diffusion equation

u_{t} = Δ \log u + λ u

$u_t=\Delta\log u+ \lambda u$ in a two-dimensional coordinate space”, TMF, 124:2 (2000), 265–278; Theoret. and Math. Phys., 124:2 (2000), 1082–1093

Citation in format AMSBIB

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\transl

\jour Theoret. and Math. Phys.

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\vol 124

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\pages 1082--1093

\crossref{https://doi.org/10.1007/BF02551079}

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Linking options:

https://www.mathnet.ru/eng/tmf638

https://doi.org/10.4213/tmf638

https://www.mathnet.ru/eng/tmf/v124/i2/p265

This publication is cited in the following 7 articles:

Zhuravlev V.M., Zolotovskii I.O., Korobko D.A., Morozov V.M., Svetukhin V.V., Yavtushenko I.O., Yavtushenko M.S., “Laser-Induced Generation of Surface Periodic Structures in Media With Nonlinear Diffusion”, Phys. Solid State, 59:12 (2017), 2313–2320
V. M. Zhuravlev, “Superposition principle and exact solutions of a nonlinear diffusion equation”, Theoret. and Math. Phys., 183:1 (2015), 478–490
V. M. Zhuravlev, I. O. Zolotovskii, V. M. Morozov, “Ob usloviyakh vozniknoveniya regulyarnykh struktur v kondensirovannykh sredakh pod deistviem vneshnego izlucheniya”, Izvestiya vysshikh uchebnykh zavedenii. Povolzhskii region. Fiziko-matematicheskie nauki, 2015, no. 3, 144–162
Igropulo V.S., “Mnogofaktornye matematicheskie modeli geterogennykh metasistem”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2011, no. 10, 70–78 Multiple-factor mathematical models of heterogeneous metasystems
Handbook of Nonlinear Partial Differential Equations, Second Edition, 2011, 1795
Zhuravlev, VM, “Autowaves in an active two-wire line with exponential current-voltage characteristic”, Journal of Experimental and Theoretical Physics, 102:3 (2006), 515
Handbook of Nonlinear Partial Differential Equations, 2003

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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