POPOVYCH, Roman, Stanislav OPANASENKO and Vyacheslav BOYKO. Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2020, vol. 484, No 1, p. "123739-1"-"123739-30", 30 pp. ISSN 0022-247X. Available from: https://dx.doi.org/10.1016/j.jmaa.2019.123739.
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Basic information
Original name Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity
Authors POPOVYCH, Roman (804 Ukraine, belonging to the institution), Stanislav OPANASENKO (804 Ukraine, guarantor) and Vyacheslav BOYKO (804 Ukraine).
Edition Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2020, 0022-247X.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10101 Pure mathematics
Country of publisher United States of America
Confidentiality degree is not subject to a state or trade secret
WWW Journal of Mathematical Analysis and Applications
RIV identification code RIV/47813059:19610/20:A0000072
Organization unit Mathematical Institute in Opava
Doi http://dx.doi.org/10.1016/j.jmaa.2019.123739
UT WoS 000508488800012
Keywords in English Group classification of differential equations; Method of furcate splitting; Diffusion-reaction equations; Lie symmetry; Equivalence group; Lie reduction
Tags MÚ
Tags International impact, Reviewed
Links EF16_027/0008521, research and development project.
Changed by Changed by: Mgr. Aleš Ryšavý, učo 28000. Changed: 6/4/2021 07:01.
Abstract
We carry out the enhanced group classification of a class of (1+1)-dimensional nonlinear diffusion-reaction equations with gradient-dependent diffusivity using the two-step version of the method of furcate splitting. For simultaneously finding the equivalence groups of an unnormalized class of differential equations and a collection of its subclasses, we suggest an optimized version of the direct method. The optimization includes the preliminary study of admissible transformations within the entire class and the successive splitting of the corresponding determining equations with respect to arbitrary elements and their derivatives depending on auxiliary constraints associated with each of required subclasses. In the course of applying the suggested technique to subclasses of the class under consideration, we construct, for the first time, a nontrivial example of finite-dimensional effective generalized equivalence group. Using the method of Lie reduction and the generalized separation of variables, exact solutions of some equations under consideration are found.
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