Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19610%2F20%3AA0000072" target="_blank" >RIV/47813059:19610/20:A0000072 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0022247X19310078?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0022247X19310078?via%3Dihub</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2019.123739" target="_blank" >10.1016/j.jmaa.2019.123739</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Enhanced group classification of nonlinear diffusion-reaction equations with gradient-dependent diffusivity

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF16_027%2F0008521" target="_blank" >EF16_027/0008521: Podpora mezinárodní mobility výzkumných pracovníků na SU</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

e-ISSN

1096-0813

Svazek periodika

484

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

30

Strana od-do

„123739-1“-„123739-30“

Kód UT WoS článku

000508488800012

EID výsledku v databázi Scopus

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