POPOVYCH, Roman, Stanislav OPANASENKO a 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, roč. 484, č. 1, s. "123739-1"-"123739-30", 30 s. ISSN 0022-247X. doi:10.1016/j.jmaa.2019.123739. 2020.
Další formáty:   BibTeX LaTeX RIS
Základní údaje
Originální název Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity
Autoři POPOVYCH, Roman (804 Ukrajina, domácí), Stanislav OPANASENKO (804 Ukrajina, garant) a Vyacheslav BOYKO (804 Ukrajina).
Vydání Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2020, 0022-247X.
Další údaje
Originální jazyk angličtina
Typ výsledku Článek v odborném periodiku
Obor 10101 Pure mathematics
Stát vydavatele Spojené státy
Utajení není předmětem státního či obchodního tajemství
WWW Journal of Mathematical Analysis and Applications
Kód RIV RIV/47813059:19610/20:A0000072
Organizační jednotka Matematický ústav v Opavě
Doi http://dx.doi.org/10.1016/j.jmaa.2019.123739
UT WoS 000508488800012
Klíčová slova anglicky Group classification of differential equations; Method of furcate splitting; Diffusion-reaction equations; Lie symmetry; Equivalence group; Lie reduction
Štítky
Příznaky Mezinárodní význam, Recenzováno
Návaznosti EF16_027/0008521, projekt VaV.
Změnil Změnil: Mgr. Aleš Ryšavý, učo 28000. Změněno: 6. 4. 2021 07:01.
Anotace
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.
VytisknoutZobrazeno: 28. 3. 2024 10:42