J 2020

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

POPOVYCH, Roman, Stanislav OPANASENKO and Vyacheslav BOYKO

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

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

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

Tags

International impact, Reviewed

Links

EF16_027/0008521, research and development project.
Změněno: 6/4/2021 07:01, Mgr. Aleš Ryšavý

Abstract

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.
Displayed: 24/12/2024 17:32