J
2020
Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity
POPOVYCH, Roman, Stanislav OPANASENKO a Vyacheslav BOYKO
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
Typ výsledku
Článek v odborném periodiku
Obor
10101 Pure mathematics
Stát vydavatele
Spojené státy
Utajení
není předmětem státního či obchodního tajemství
Kód RIV
RIV/47813059:19610/20:A0000072
Organizační jednotka
Matematický ústav v Opavě
Klíčová slova anglicky
Group classification of differential equations; Method of furcate splitting; Diffusion-reaction equations; Lie symmetry; Equivalence group; Lie reduction
Příznaky
Mezinárodní význam, Recenzováno
Návaznosti
EF16_027/0008521, projekt VaV.
V originále
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.
Zobrazeno: 26. 12. 2024 00:03