Geodesic
Lambert function and exact solutions of nonlinear parabolic equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 13-20

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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
Mots-clés : exact solutions. 
@article{IVM_2019_8_a1,
     author = {A. A. Kosov and E. I. Semenov},
     title = {Lambert function and exact solutions of nonlinear parabolic equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {13--20},
     publisher = {mathdoc},
     number = {8},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2019_8_a1/}
}
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A. A. Kosov; E. I. Semenov. Lambert function and exact solutions of nonlinear parabolic equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2019), pp. 13-20. http://geodesic.mathdoc.fr/item/IVM_2019_8_a1/